J Wang

Robust adaptive stabilization by delay under state parametric uncertainty and measurement bias

An output robust adaptive control is designed for a class of Lipschitz nonlinear systems under assumption that the measurements are available with a constant bias and the state equations linearly parameterized by unknown parameters and external disturbances. A dynamic state reconstruction (synthesis of an observer) is avoided by using delayed values of the output in the feedback and adaptation laws. The analysis of robust stability for the resulted time-delay system is performed by using the Lyapunov-Krasovskii approach. The control and adaptation gains can be selected as a solution of the proposed linear matrix inequalities. This research is motivated by a nonlinear pendulum control problem, and the efficacy of the developed control is demonstrated on this application through experiments.

I. INTRODUCTION

Design of identification algorithms, estimators and regulators for dynamical systems are fundamental and complex problems studied in the control theory. Since in all engineering applications the models of the plants are subjected by uncertainty of different kinds (e.g., exogenous unknown inputs, measurement noises and perturbations, unknown parameters or unmodeled dynamics), the design and analysis methods are classified by their abilities to undertake the plant's incertitude [START_REF] Khalil | Nonlinear Control[END_REF]. In particular, the group of methods belonging to the adaptive control theory deals with compensation of influence on estimation and stabilization of unknown parameters [START_REF] Sastry | Adaptive Control: Stability, Convergence and Robustness[END_REF].

In many cases, due to information transmission in the input-output channels, delays appear in the dynamics of the controlled plant [START_REF] Richard | Time-delay systems: an overview of some recent advances and open problems[END_REF], [START_REF] Yang | Review of stability and stabilization for impulsive delayed systems[END_REF]. Influence of a delay on the system stability is vital in many cases [START_REF] Gu | Stability of Time-Delay Systems[END_REF], [START_REF] Fridman | Introduction to Time-Delay Systems: Analysis and Control[END_REF], and it usually leads to degradation of the performances of regulation or estimation [START_REF] Fridman | Introduction to Time-Delay Systems: Analysis and Control[END_REF]. However, in some cases introduction of a delay may result in an improvement of the system transients (see [START_REF] Kharitonov | Static output feedback stabilization: necessary conditions for multiple delay controllers[END_REF], [START_REF] Fridman | Delay-induced stability of vector secondorder systems via simple Lyapunov functionals[END_REF], [START_REF] Fridman | Stabilization by using artificial delays: An LMI approach[END_REF], [START_REF] Efimov | Homogeneity of neutral systems and accelerated stabilization of a double integrator by measurement of its position[END_REF], [START_REF] Nekhoroshikh | On output-based accelerated stabilization of a chain of integrators: Implicit Lyapunov-Krasovskii functional approach[END_REF] and the references therein). The idea of these papers is that unmeasured components of the state can be calculated using delayed values of the measured variables, which allow a design of observer to be passed by, but at the price of a more sophisticated stability analysis (that is based in these works on an appropriate Lyapunov-Krasovskii functional, and another possible approach is the Lyapunov-Razumikhin method; and the complexity comes from the fact that the closed-loop system becomes unstable in the delay-free case).

The goal of this note is to extend the results obtained in [START_REF] Fridman | Delay-induced stability of vector secondorder systems via simple Lyapunov functionals[END_REF], [START_REF] Fridman | Stabilization by using artificial delays: An LMI approach[END_REF] for linear systems to adaptive stabilization of a class of nonlinear systems, which include a globally Lipschitz nonlinearity, unknown parameters, exogenous disturbances, and have a part of the measurements available with a constant bias, which is induced by a sensor error (a preliminary version of this study appears in [START_REF] Efimov | Adaptive stabilization by delay with biased measurements[END_REF] without proofs and additional details). Since for embedded control and estimation solutions, the amount of computations needed for realization is a critical resource (more important than the used memory in some scenarios), in this note we avoid to design an (reduced order) observer for the state, but introduce delayed measurements in the feedback and adaptation algorithm. The closed-loop system becomes time-delayed, then stability analysis of the regulation error is based on the Lyapunov-Krasovskii functional proposed in [START_REF] Fridman | Delay-induced stability of vector secondorder systems via simple Lyapunov functionals[END_REF], [START_REF] Fridman | Stabilization by using artificial delays: An LMI approach[END_REF], whose properties can be assessed by investigating linear matrix inequalities (LMIs).

It is important to note that there exist papers devoted to adaptive control of time-delay systems as, for example, [START_REF] Pepe | Adaptive output tracking for a class ofnonlinear time delay systems[END_REF], [START_REF] Mirkin | Robust adaptive output-feedback tracking for a class of nonlinear time-delayed plants[END_REF], [START_REF] Selivanov | Passification-based adaptive control: Uncertain input and output delays[END_REF] (the uncertain parameters appear in the state equation only), or papers dealt with adaptive/robust control for systems with multiplicative uncertain parameters in the output equation [START_REF] Zhang | A K-filter-based adaptive control for nonlinear systems with unknown parameters in state and output equations[END_REF], [START_REF] Zhang | Robust output feedback control of polynomial growth nonlinear systems with measurement uncertainty[END_REF] (without presence of time delays) or [START_REF] Mazenc | Stabilization and robustness analysis for a chain of saturating integrators with imprecise measurements[END_REF], but to the best of our knowledge there is no theory dealing with time-delay systems subjected to parametric uncertainty in the state dynamics and the output measurements simultaneously.

The selected problem statement is not artificial, since it can be motivated by a mechanical balancing system application, e.g., stabilization of a walking robot, where a constant bias distorts the angular position measurements. This application is described with more details in [START_REF] Aranovskiy | Differentiator-based velocity observer with sensor bias estimation: an inverted pendulum case study[END_REF], where the authors proposed a nonlinear bias and velocity estimator proving local asymptotic convergence. In this paper, we are solving the same problem by designing a delay-based adaptive algorithm, which stabilizes the pendulum in the presence of the measurement bias 1 . We also experimentally verify the proposed solution with the inverted pendulum hardware setup equivalent to the one used in [START_REF] Aranovskiy | Differentiator-based velocity observer with sensor bias estimation: an inverted pendulum case study[END_REF].

The outline of this article is as follows. The preliminaries are given in Section II. The problem statement is introduced in Section III. The adaptive control design and stability con-ditions are presented in Section IV. A nonlinear pendulum application is considered in Section V. The symbol 1, m is used to denote a sequence of integers 1, ..., m. For a symmetric matrix P ∈ R n×n , the minimum and the maximum eigenvalues are denoted as λ min (P ) and λ max (P ), respectively. For a matrix A ∈ R n×m , |A| = λ max (A A) is the induced norm. The identity matrix of dimension n × n is denoted by I n .

A. Neutral time-delay systems

Consider an autonomous functional differential equation of neutral type with inputs [START_REF] Kolmanovsky | Stability of functional differential equations[END_REF]:

ẋ(t) = f (x t , ẋt , d(t)) (1)
for almost all t ≥ 0, where x(t) ∈ R n and

x t ∈ W 1,∞ [-τ,0]
is the state function,

x t (s) = x(t + s), -τ ≤ s ≤ 0, with ẋt ∈ L n [-τ,0] ; d(t) ∈ R m is the external input, d ∈ L m ∞ ; f : W 1,∞ [-τ,0] × L n [-τ,0] × R m → R n is a
continuous functional, that is globally Lipschitz in the second variable with a constant smaller than 1, ensuring forward uniqueness and existence of the system solutions [START_REF] Kolmanovsky | Stability of functional differential equations[END_REF]. We assume f (0, 0, 0) = 0. For the initial function

x 0 ∈ W 1,∞ [-τ,0] and disturbance d ∈ L m
∞ denote a unique solution of the system (1) by x(t, x 0 , d), which is an absolutely continuous function of time defined on some maximal interval [-τ, T ) for T > 0, then

x t (x 0 , d) ∈ W 1,∞ [-τ,0]
represents the corresponding state function with x t (s, x 0 , d) = x(t + s, x 0 , d) for -τ ≤ s ≤ 0.

Given a locally Lipschitz continuous functional V : R × W 1,∞ [-τ,0] × L n [-τ,0] → R + define its derivative in the Driver's form:

D + V (t, φ, d) = lim h→0 + sup 1 h [V (t + h, x h (φ, d), ẋh (φ, d)) -V (t, φ, φ)],
where x h (φ, d) is a solution of the system (1) for

φ ∈ W 1,∞ [-τ,0]
and d(t) = d for all t ≥ 0 and some d ∈ R m .

B. ISS of time delay systems

The input-to-state stability (ISS) property is an extension of the conventional stability paradigm to the systems with external inputs [START_REF] Teel | Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem[END_REF], [START_REF] Pepe | A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems[END_REF], [START_REF] Fridman | On input-to-state stability of systems with time-delay: A matrix inequalities approach[END_REF]. Definition 1. [START_REF] Pepe | A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems[END_REF], [START_REF] Fridman | On input-to-state stability of systems with time-delay: A matrix inequalities approach[END_REF] The system (1) is called practical ISS, if for all x 0 ∈ W 1,∞ [-τ,0] and d ∈ L m ∞ there exist q ≥ 0, β ∈ KL and γ ∈ K such that

|x(t, x 0 , d)| ≤ β( x 0 W , t) + γ(||d|| ∞ ) + q ∀t ≥ 0. If q = 0 then (1) is called ISS.
For establishment of this stability property, the Lyapunov-Krasovskii theory can be used [START_REF] Pepe | A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems[END_REF], [START_REF] Fridman | On input-to-state stability of systems with time-delay: A matrix inequalities approach[END_REF], [START_REF] Efimov | Homogeneity of neutral systems and accelerated stabilization of a double integrator by measurement of its position[END_REF].

Definition 2. A locally Lipschitz continuous functional V : R + ×W 1,∞ [-τ,0] ×L n [-τ,0] → R + (i.e., V (t, φ, φ)) is called simple if D + V (t, φ, d) is independent on φ.
For instance, a locally Lipschitz functional V : R + × W 1,∞ [-τ,0] → R + is simple, another example of a simple functional is given in Theorem 8 below. Definition 3. A locally Lipschitz continuous functional V :

R + × W 1,∞ [-τ,0] × L n [-τ,0] → R + is called practical ISS Lyapunov-Krasovskii functional for the system (1) if it is simple and there exist r ≥ 0, α 1 , α 2 ∈ K ∞ and α, χ ∈ K such that for all t ∈ R + , φ ∈ W 1,∞ [-τ,0] and d ∈ R m : α 1 (|φ(0)|) ≤ V (t, φ, φ) ≤ α 2 ( φ W ), V (t, φ, φ) ≥ max{r, χ(|d|)} =⇒ D + V (t, φ, d) ≤ -α(V (t, φ, φ)).
If r = 0 then V is an ISS Lyapunov-Krasovskii functional.

Theorem 4. [START_REF] Fridman | On input-to-state stability of systems with time-delay: A matrix inequalities approach[END_REF] If there exists a (practical) ISS Lyapunov-Krasovskii functional for the system (1), then it is (practical) ISS with γ = α -1 1 • χ. Converse results for Theorem 4 can be found in [START_REF] Pepe | Lyapunov-Krasovskii characterization of the input-to-state stability for neutral systems in Hale's form[END_REF], [START_REF] Efimov | Converse Lyapunov-Krasovskii theorem for ISS of neutralsystems in Sobolev spaces[END_REF].

III. ROBUST OUTPUT ADAPTIVE REGULATION WITH

BIASED MEASUREMENTS Consider a nonlinear system for the time t ≥ 0:

ẋ1 (t) = x 2 (t), ẋ2 (t) = A 21 x 1 (t) + A 22 x 2 (t) + A 23 x 3 (t) +B 1 (u(t) + Ω(t)θ 2 ) + L 1 φ(x(t)) + d 1 (t), ẋ3 (t) = A 31 x 1 (t) + A 32 x 2 (t) + A 33 x 3 (t) (2) +B 2 (u(t) + Ω(t)θ 2 ) + L 2 φ(x(t)) + d 2 (t), y 1 (t) = x 1 (t) + θ 1 , y 2 (t) = x 3 (t),
where x 1 (t) ∈ R n and x 2 (t) ∈ R n are the position and velocity, respectively,

x 3 (t) ∈ R p is an additional state, x(t) = [x 1 (t) x 2 (t) x 3 (t)] ∈ R 2n+p is the total state vector of (2), the initial conditions x(0) = x 0 ∈ R 2n+p are unknown; u(t) ∈ R m is the control input; y(t) = [y 1 (t) y 2 (t)] ∈ R n+p is the output available for measure- ments, d(t) = [d 1 (t) d 2 (t)] ∈ R n+p is the disturbance with d ∈ L n+p ∞ ; θ 1 ∈ R n is the vector of biases in the measurements of the position x 1 (t), θ 2 ∈ R r is the vector of uncertain parameters in the state dynamics, θ = [θ 1 θ 2 ] ∈ R n+r ,
the regressor Ω : R + → R m×r is a known continuous matrix function; the nonlinearity φ can be partitioned as

φ(x) = φ 1 (x) φ 2 (x 3 ) ,
where φ 1 : R 2n+p → R s1 and φ 2 : R p → R s2 , then we can decompose

L 1 = [L 11 L 12 ], L 2 = [L 21 L 22 ]
, and φ(x) is assumed to be Lipschitz continuous; all the matrices are constant and known having the corresponding dimensions. Therefore, the considered system is subjected by unknown inputs d(t), it contains unknown parameters θ (part of them corrupt the measurements), and the equations of ( 2) are nonlinear and time-varying due to the presence of φ and Ω, respectively. Many mechanical systems (subsystem with coordinates x 1 and x 2 ) in connection with a motor, sensor or actuator (the variable x 3 ) can be represented in the form [START_REF] Sastry | Adaptive Control: Stability, Convergence and Robustness[END_REF].

The goal is to design an (dynamical) output control input u(t) = u(y 1 (t), y 2 (t), Ω(t)) ensuring a practical ISS property of the closed loop system for all x 0 ∈ R 2n+p and all d ∈ L n+p ∞ under the restriction to minimize the computational complexity of the algorithm (in order to be able to use the proposed solution as a component of an embedded system). Remark 5. Note that a change of variables 2) to a dynamics with two purely measured states,

x1 (t) = x 1 (t)+θ 1 , xi (t) = x i (t) for i = 2, 3 transforms (
y 1 (t) = x1 (t), y 2 (t) = x3 (t),
but it makes the equations nonlinearly parameterized by θ 1 . Extending this state by x4 (t) = θ 1 poses in question the observability of such an augmented system with ẋ4 (t) = 0, which becomes dependent on the characteristics of φ.

We need the following hypothesis on the properties of (2):

Assumption 1. For the regressor function Ω(t) there is a known upper bound Ω ≥ 0 such that sup t≥0 |Ω(t)| ≤ Ω.

The function φ satisfies a sector condition φ (x)φ(x) ≤ x Υx for all x ∈ R 2n+p and a symmetric matrix 0 ≤ Υ ∈ R (2n+p)×(2n+p) . The function φ 2 : R p → R s2 is known.

Under the introduced restriction on φ the system (2) has well-defined solutions for all t ≥ 0 for any x 0 ∈ R 2n+p and any d ∈ L n+p ∞ [START_REF] Khalil | Nonlinear Control[END_REF]. Remark 6. The regressor Ω can be a nonlinear function of any measured information, e.g., Ω(t) = Ω(t, y 1 (t), y 2 (t), u(t)), provided that it is globally bounded.

IV. MAIN RESULTS

Due to a rather complicated structure of the considered system and introduced uncertainty, clearly, for realization of a robustly stabilizing control it is necessary to use the full state x(t) information. Consequently, it is required to design an estimator for x 1 (t), which is measured with an unknown bias θ 1 , and for its velocity x 2 (t). Facing all uncertain terms presented in (2), i.e. θ 2 and d(t), such an observation problem becomes rather intriguing, and a corresponding observer solving these issues will be also complex and nonlinear. In [START_REF] Kharitonov | Static output feedback stabilization: necessary conditions for multiple delay controllers[END_REF], [START_REF] Fridman | Delay-induced stability of vector secondorder systems via simple Lyapunov functionals[END_REF], [START_REF] Fridman | Stabilization by using artificial delays: An LMI approach[END_REF] an approach is presented for design of a linear delayed output static control for a linear system, which avoids a state observer design by introducing the estimates of x(t) through delayed output y(t) values. Hence, such a method has a low computational capacity (since for delay operation only memory is needed). In this work we will follow the same approach.

Defining

x 1 (t -h) = x 1 (0) for t ∈ [0, h],
where h > 0 is the delay, the control algorithm proposed in this paper is

u(t) = -(K 1 + K 2 )y 1 (t) + K 2 y 1 (t -h) (3) -K 3 y 2 (t) -K 4 φ 2 (y 2 (t)) + K 1 θ1 (t) -Ω(t) θ2 (t),
where θ1 (t) ∈ R n and θ2 (t) ∈ R r are the estimates of θ 1 and θ 2 , respectively; K i ∈ R m×n for i = 1, 2, K 3 ∈ R m×p and K 4 ∈ R m×s2 are the control gains to be derived. Similarly, an adaptive law for θ1 (t) can be synthesized:

θ1 (t) = (F 1 + F 2 )y 1 (t) -F 2 y 1 (t -h) (4) +F 3 y 2 (t) + F 4 φ 2 (y 2 (t)) -F 1 θ1 (t),
where

F i ∈ R n×n for i = 1, 2, F 3 ∈ R n×p and F 4 ∈ R n×s2
are the adaptation gains which will be defined later. An adaptive law for θ2 (t) is more sophisticated, and such a choice of the structure will become clear from the stability analysis given next:

θ2 (t) = Ω (t)[(S 1 + S 2 )y 1 (t) -S 2 y 1 (t -h) (5) +S 3 y 2 (t) + S 4 φ 2 (y 2 (t)) -S 1 θ1 (t)] -S 5 θ2 (t),
where S i ∈ R m×n for i = 1, 2, S 3 ∈ R m×p , S 4 ∈ R m×s2 and S 5 ∈ R r×r are also the adaptation gains. Remark 7. There is also an algebraic way to solve the problem of estimation of unknown values θ 1 , θ 2 and signals x 1 (t), x 2 (t) (in the framework of indirect adaptive control), which is based on some structural restrictions and auxiliary filtering. Indeed, let p = n and J 1 L 11 = J 2 L 21 for some matrices J 1 and J 2 , then define

ζ(t) = J 1 x 2 (t) -J 2 x 3 (t) with ζ(t) = Y 1 (y 1 (t) -θ 1 ) + Y 2 ẏ1 (t) + Y 3 y 2 (t) + Y 4 (u(t) +Ω(t)θ 2 ) + Y 5 φ 2 (y 2 (t)) + J 1 d 1 (t) -J 2 d 2 (t),
where

Y 1 = J 1 A 21 -J 2 A 31 , Y 2 = J 1 A 22 -J 2 A 32 , Y 3 = J 1 A 23 -J 2 A 33 , Y 4 = J 1 B 1 -J 2 B 2 , Y 5 = J 1 L 12 -J 2 L 22 .
Let also for brevity

d 1 (t) = 0, d 2 (t) = 0, Y 1 = 0. Note that by construction ζ(t) = J 1 ÿ1 (t) -J 2 ẏ2 (t)
, and equating the expressions for ζ(t) we obtain:

ζ(t) = -Y 1 θ 1 + Y 4 Ω(t)θ 2 ,
which is a linear regressor model with respect to unknown parameters θ 1 and θ 2 that can be used for their identification, where ζ(t) and Ω(t) variables calculated as

Ω(t) = λ 2 (s + λ) 2 Ω(t), ζ(t) = J 1 λ 2 s 2 (s + λ) 2 y 1 (t) -Y 2 λ 2 s (s + λ) 2 y 1 (t) -J 2 λ 2 s (s + λ) 2 y 2 (t) - λ 2 (s + λ) 2 [Y 1 y 1 (t) + Y 3 y 2 (t) + Y 4 u(t) + Y 5 φ 2 (y 2 (t))]
with s being the differentiating operator and λ > 0 is a tuning parameter of the filters. Inversely, if

d 1 (t) = 0, d 2 (t) = 0, Y 1 = 0, θ 2 = 0, then ψ(t) = 1 s + 1 ζ(t) = J 1 s s + 1 y 1 (t) -J 2 1 s + 1 y 2 (t)
is a variable that we can calculate, and

ψ(t) = ζ(t) - 1 s + 1 ζ(t) = ζ(t) - 1 s + 1 [Y 2 ẏ1 (t) +Y 3 y 2 (t) + Y 4 u(t) + Y 5 φ 2 (y 2 (t))].
Hence, for a nonsingular J 1 we obtain x 2 (t) = J -1 1 ψ(t), where

ψ(t) = ψ(t) + Y 2 s s + 1 y 1 (t) + 1 s + 1 [Y 3 y 2 (t) +Y 4 u(t) + Y 5 φ 2 (y 2 (t))] + J 2 y 2 (t)
can be calculated using filters. If d 1 (t) = 0 and d 2 (t) = 0, then these approaches lead to a reconstruction of unknown parameters and variables corrupted by noises, and robust estimation tools should be applied. Next, a control design has to be performed. A drawback of such solutions is also their computational complexity comparing to (3), ( 4), [START_REF] Gu | Stability of Time-Delay Systems[END_REF], where just additional adaptation algorithms (observers or filters) are introduced to calculate θ1 (t) and θ2 (t) in order to compensate the influence of θ 1 and θ 2 .

It is worth noting that a complexity of ( 3), ( 4), ( 5) comes from another side. Initially the system (2) is delay-free (the state x(t) ∈ R 2n+p ), then (3), ( 4), ( 5) introduces the delay h and transforms the system into the retarded type time-delay dynamics [START_REF] Fridman | Introduction to Time-Delay Systems: Analysis and Control[END_REF] (the state function is from C 2n+p [-h,0] ), while for the stability analysis we will perform below an additional transformation of the closed-loop system to the neutral type (with the state from W 1,∞ [-h,0] ). Therefore, (3), ( 4), (5) needs a rather sophisticated analysis, but it allows a simple realization.

The restrictions on selection the control and adaptation gains, and the conditions to check, are given in the following theorem. Theorem 8. Let Assumption 1 be satisfied. If for given K i , F i with i = 1, 4 and S i with i = 1, 5 the system of linear matrix inequalities

Q ≤ 0, P = P > 0, α > 0, β > 0, δ > 0, η > 0, (6)
M M ≤ ρIs 1 +s 2 , 4 e -h h 2 In ≥ αB B S = G P + qh 2 G Γ ΓA, S2 = -qh 2 G Γ ΓB, S4 = qh 2 G Γ ΓM Q =        Q11 N N N M -αqI3n+p M N M M -βI3n+p 0 0 0 N M M 0 0 0 0 N 0 0 M 0 0 M 0 Q44 0 -S5 0 M -(η -qh 2 )I3n+p 0 -S 5 0 -δIr        , Q11 = P A + A P + qh 2 A Γ ΓA + ρβC ΥC + P, Q44 = -2S5 + (qh 2 |B1| 2 Ω2 + )Ir, N = P + qh 2 A Γ Γ, M = qh 2 Γ Γ,
is feasible with respect to P , α, β, δ and η for some q > 0, > 0 and ρ > 0, where

A =    0 In 0 0 A21 -B1K1 A22 -hB1K2 A23 -B1K3 B1K1 A31 -B2K1 A32 -hB2K2 A33 -B2K3 B2K1 F1 hF2 F3 -F1    , B =    0 B1K2 B2K2 -F2    , G =    0 B1 B2 0    , D =    0 In Ip 0    , M =    0 0 L11 L12 -B1K4 L21 L22 -B2K4 0 F4    , C =   In 0 0 0 0 In 0 0 0 0 Ip 0   , S = S1 hS2 S3 -S1 , S4 = 0 S4 , Γ = 0 In 0 0 .
Then the system (2) with the control (3) and adaptive laws (4), ( 5) is practically ISS.

Proof: Following the ideas of [START_REF] Fridman | Delay-induced stability of vector secondorder systems via simple Lyapunov functionals[END_REF], [START_REF] Fridman | Stabilization by using artificial delays: An LMI approach[END_REF] note that y 1 (t-h) = y 1 (t)-h ẏ1 (t)+R(t) for R(t) = t t-h (s-t+h)ÿ 1 (s)ds, which can be easily checked by applying integration by parts, then the expressions for (3), ( 4), ( 5) can be represented as follows:

u(t) = -K 1 y 1 (t) -hK 2 ẏ1 (t) + K 2 R(t) -K 3 y 2 (t) -K 4 φ 2 (y 2 (t)) +K 1 θ1 (t) -Ω(t) θ2 (t) = -K 1 x 1 (t) -hK 2 x 2 (t) + K 2 R(t) -K 3 x 3 (t) -K 4 φ 2 (x 3 (t)) +K 1 θ1 (t) -Ω(t) θ2 (t), θ1 (t) = F 1 y 1 (t) + hF 2 ẏ1 (t) -F 2 R(t) +F 3 y 2 (t) + F 4 φ 2 (y 2 (t)) -F 1 θ1 (t) = F 1 x 1 (t) + hF 2 x 2 (t) -F 2 R(t) +F 3 x 3 (t) + F 4 φ 2 (x 3 (t)) -F 1 θ1 (t), θ2 (t) = Ω (t)[S 1 y 1 (t) + hS 2 ẏ1 (t) -S 2 R(t) +S 3 y 2 (t) + S 4 φ 2 (y 2 (t)) -S 1 θ1 (t)] -S 5 θ2 (t) = Ω (t)[S 1 x 1 (t) + hS 2 x 2 (t) -S 2 R(t) +S 3 x 3 (t) + S 4 φ 2 (x 3 (t)) -S 1 θ1 (t)] -S 5 θ2 (t),
where we substituted the expressions of the outputs y 1 (t) and y 2 (t) (note that ẏ1 (t) = x 2 (t) since θ 1 is constant), and θ1 (t) = θ1 (t) -θ 1 is the adaptation error for θ1 (t). Similarly we define θ2 (t) = θ2 (t) -θ 2 as the adaptation error for θ2 (t), and for z(t) = [x (t) θ 1 (t)] the closed loop dynamics take the form:

ż(t) = Az(t) + BR(t) -GΩ(t) θ2 (t) (7) +Mφ(Cz(t)) + Dd(t), θ2 (t) = Ω (t)[Sz(t) -S 2 R(t) +S 4 φ(Cz(t))] -S 5 θ2 (t) -S 5 θ 2 ,
where all matrices are defined in the formulation of the theorem. Obviously, due to presence of R(t), which contains the state derivative Γ ż(s) with s ∈ [t -h, t], the system ( 7) is of neutral type, then z t ∈ W 1,∞ [-h,0] is the state together with θ2 (t) ∈ R r . Then, in order to analyze ISS property of ( 7) with respect to the inputs d(t) and θ 2 , let us consider a Lyapunov-Krasovskii functional candidate:

V (z t , żt , θ2 (t)) = z (t)P z(t) + qW (z t , żt ) + θ 2 (t) θ2 (t), W (z t , żt ) = t t-h e (s-t) (s -t + h) 2 ż (s)Γ Γ ż(s)ds,
where P = P > 0 and q > 0 are solutions of ( 6) and > 0 (if we would substitute the expression of Γ ż(s) from ( 7), then V will be a function of the disturbance d, hence, the neutral interpretation of ( 2), ( 3), ( 4), ( 5) is obligatory). For W (t) = W (z t , żt ) a direct computation gives:

Ẇ (t) = -2 t t-h e (s-t) (s -t + h) ż (s)Γ Γ ż(s)ds +h 2 ż (t)Γ Γ ż(t) -W (t),
and applying Jensen's inequality [START_REF] Fridman | Introduction to Time-Delay Systems: Analysis and Control[END_REF] we obtain:

t t-h e (s-t) (s -t + h) ż (s)Γ Γ ż(s)ds ≥ 2 e -h h 2 R (t)R(t), then Ẇ (t) ≤ h 2 ż (t)Γ Γ ż(t) -4 e -h h 2 R (t)R(t) -W (t).
The full derivative of V (t) = V (z t , żt , θ2 (t)) for ( 7) can now be estimated as follows:

V (t) ≤ z (t)P ż(t) + ż (t)P z(t) + qh 2 ż (t)Γ Γ ż(t) -4q e -h h 2 R (t)R(t) -q W (t) + 2 θ 2 (t) θ2(t) ≤ ξ (t)Q(t)ξ(t) -V (t) -qR (t)(4 e -h h 2 -αB B)R(t) +β[φ (Cz(t))M Mφ(Cz(t)) -ρz (t)C ΥCz(t)] +ηd (t)d(t) + δθ 2 θ2 +2 θ 2 (t)Ω (t)[(S -G P -qh 2 G Γ ΓA)z(t) -(S2 + qh 2 G Γ ΓB)R(t) +(S4 -qh 2 G Γ ΓM)φ(Cz(t))],
where

ξ(t) = [z (t) R (t)B φ (Cz(t))M θ 2 (t) d (t)D θ 2 ] , Q(t) =        Q11 N N N M -αqI3n+p M N M M -βI3n+p 0 0 0 N M M 0 0 0 0 N 0 0 M 0 0 M 0 E(t) 0 -S5 0 M -(η -qh 2 )I3n+p 0 -S 5 0 -δIr        , E(t) = -2S5 + qh 2 H (t)H(t) + Ir, H(t) = ΓGΩ(t),
where the matrices M and N are introduced in the formulation of the theorem, the parameters α, β, δ and η come from [START_REF] Fridman | Introduction to Time-Delay Systems: Analysis and Control[END_REF], and the only inequality used on the last step is Therefore, the upper estimate on the derivative of the Lyapunov-Krasovskii functional can be rewritten as follows:

θ 2 (t
V (t) ≤ ξ (t)Qξ(t) -V (t) + ηd (t)d(t) + δθ 2 θ 2 ,
where we used the fact that

|H(t)| ≤ |B 1 | Ω from Assumption 1, then E(t) ≤ -2S 5 + (qh 2 |B 1 | 2 Ω2 + )I r .
Finally, since by the conditions of the theorem Q ≤ 0, we obtain

V (t) ≤ -V (t) + ηd (t)d(t) + δθ 2 θ 2 , (8)
which implies that V is an ISS Lyapunov-Krasovskii functional for (7) and the system possesses ISS property with respect to the inputs d(t) and θ 2 (practical ISS with respect to the input d(t)) due to Theorem 4 provided that there exist

α 1 , α 2 , α 1 , α 2 ∈ K ∞ such that α 1 (|z(t)|) + α 1 (| θ2 (t)|) ≤ V (z t , żt , θ2 (t)) ≤ α 2 ( z t W ) + α 2 (| θ2 (t)|)
for all z t ∈ W 1,∞ [-h,0] and θ2 (t) ∈ R r . Obviously, α 1 (s) = λ min (P )s 2 , α 1 (s) = α 2 (s) = s 2 , and in order to evaluate α 2 let us consider

W (z t , żt ) ≤ t t-h (s -t + h) 2 ż (s)Γ Γ ż(s)ds ≤ h 2 t t-h ż (s)Γ Γ ż(s)ds ≤ h 3 sup s∈[t-h,t] ż (s)Γ Γ ż(s) ≤ h 3 żt 2 ≤ h 3 z t 2 W , then α 2 (s) = λ max (P )s 2 + qh 3 s 2 .
The conditions of the theorem connect the control parameters to be tuned (the gains K i , F i , S i and the admissible delay h), the auxiliary constants (q > 0, > 0, ρ > 0) and the variables of linear matrix inequalities (Q ≤ 0, P > 0, α > 0, β > 0, δ > 0 and η > 0), which are obtained applying numerical solvers to [START_REF] Fridman | Introduction to Time-Delay Systems: Analysis and Control[END_REF]. By arguments of [START_REF] Fridman | Delay-induced stability of vector secondorder systems via simple Lyapunov functionals[END_REF], [START_REF] Fridman | Stabilization by using artificial delays: An LMI approach[END_REF] it can be shown that the inequalities in (6) are always feasible for a sufficiently small value of h.

Remark 9. As it follows from the proof of Theorem 8 and the estimate (8) calculated for the derivative of the Lyapunov-Krasovskii functional V , if there is no disturbance and the parametric uncertainty is presented by the measurement bias only (i.e., d = 0 and θ 2 = 0), then the studied closedloop system is globally asymptotically stable. Therefore, the value of the bias θ 1 can be exactly identified by the adjusted parameter θ1 (t), and such an achievement is possible without imposing any excitation requirement since the bias value is contained in the output y 1 directly.

Remark 10. The presentation above is given by factorizing the LMIs in the briefest way, which, however, may be more conservative. For example, taking

ξ(t) = [z (t) R (t) φ (Cz(t)) θ 2 (t) d (t) θ 2 ]
we obtain that if for given K i , F i with i = 1, 4 and S i with i = 1, 5 the system of linear matrix inequalities

Q ≤ 0, P = P > 0, α > 0, β > 0, δ > 0, η > 0, (9)
S = G P + qh 2 G Γ ΓA, S 2 = -qh 2 G Γ ΓB, S 4 = qh 2 G Γ ΓM Q =           Q 11 N B N M B N B M B -4q e -h h 2 In B M M M N M M B M M M -βI s 1 +s 2 0 0 0 D N D M B D M M 0 0 0 0 N D 0 0 B M D 0 0 M M D 0 Q 44 0 -S 5 0 D M D -(η -qh 2 )I n+p 0 -S 5 0 -δIr          , Q 11 = P A + A P + qh 2 A Γ ΓA + βC ΥC + P,
is feasible with respect to P , α, β, δ and η for some q > 0 and > 0 (where the meaning of other variables is the same as in the formulation of Theorem 8), then the system (2) with the control (3) and adaptive laws (4), ( 5) is also practically ISS. However, it is worth to stress a more nonlinear nature of (9) comparing with [START_REF] Fridman | Introduction to Time-Delay Systems: Analysis and Control[END_REF].

Remark 11. If appearance of an additional noise v ∈ L n+p ∞ in the output measurements of (2) is assumed:

y 1 (t) = x 1 (t) + θ 1 + v 1 (t), y 2 (t) = x 3 (t) + v 2 (t) with v(t) = [v 1 (t) v 2 (t)] ∈ R n+p ,
then it results in a linear perturbation of the control (3) (except for the nonlinearity φ 2 (y 2 (t)), but since it is supposed to be Lipschitz, the treatment of this term will not change the conclusion), whose influence can be masked by d. The adaptation algorithms (4) and ( 5) contain already the negative robustifying feedbacks proportional to θ1 (t) and θ2 (t), respectively (they are included to counteract the disturbance d). Hence, an additive measurement noise v will not impact stability, and the ISS property can be proven for the closed-loop system with respect to both, the state perturbation d and the measurement noise v, by applying the same arguments.

In Theorem 8 it is assumed that the control and adaptation gains K i , F i , S i are already given. A way to obtain them consists in solution of the stabilization problem under assumption that the state is measured, and next to look for the delay h that verifies the above restrictions. However, by introducing additional mild restrictions we can reformulate the conditions of Theorem 8 by considering the control and adaptation gains K i , F i , S i as solutions of LMIs: Corollary 12. Let Assumption 1 be satisfied for Υ > 0, if the system of linear matrix inequalities

Q ≤ 0, P -1 = P - ≥ 0, α > 0, β > 0, δ > 0, η > 0, (10)
ρIs 1 +s 2 M M I3n+p ≥ 0, I3n+p P -1 C CP -1 1 ρ Υ -1 ≥ 0, 2P -1 -α 4 e h ∆ -1 U G -W I GU -IW I3n+p ≥ 0, ∆ = c diag[In, c -1 In, Ip, In], Σ = G + qh 2 B 1 (ΓA0P -1 -B1U ), Σ2 = -qh 2 B 1 B1U2, 0 S4 = qh 2 B 1 L11 L12 -B1K4 Q =          Q11 I3n+p I3n+p 0 I3n+p -αqI3n+p 0 0 I3n+p 0 -βI3n+p 0 0 0 0 Q44 I3n+p 0 0 0 0 0 0 -S 5 Q 17 -Γ -Γ 0 I3n+p 0 Q17 0 0 -Γ 0 0 -Γ 0 -S5 0 -(η -qh 2 )I3n+p 0 -Γ 0 -δIr 0 -Γ 0 -1 qh 2 In           , Q11 = A0P -1 + P -1 A 0 -GU -U G +IW + W I + βI3n+p + P -1 , Q17 = -P -1 A 0 Γ + U B 1 , Q44 = -2S5 + (qh 2 |B1| 2 Ω2 + )Ir,
is feasible with respect to P -1 , U, W, Σ, K 4 , F 4 , S 4 , S 5 , α, β, η and δ for some given q > 0, c > 0, > 0, µ > 0 and ρ > 0, where

A 0 =     0 I n 0 0 A 21 A 22 A 23 0 A 31 A 32 A 33 0 0 0 0 0     , I =     0 0 0 I n     ,
and the matrices B, G, D, M, C and Γ are defined in Theorem 8. Then for

K 1 hK 2 K 3 K 5 = UP, F 1 hF 2 F 3 F 5 = WP, S 1 hS 2 S 3 S 6 = ΣP,
the system (2) with the control and adaptive laws

u(t) = -(K 1 + K 2 )y 1 (t) + K 2 y 1 (t -h) (11) -K 3 y 2 (t) -K 4 φ 2 (y 2 (t)) -K 5 θ1 (t) -Ω(t) θ2 (t), θ1 (t) = (F 1 + F 2 )y 1 (t) -F 2 y 1 (t -h) (12) +F 3 y 2 (t) + F 4 φ 2 (y 2 (t)) + F 5 θ1 (t), θ2 (t) = Ω (t)[(S 1 + S 2 )y 1 (t) -S 2 y 1 (t -h) (13
) +S 3 y 2 (t) + S 4 φ 2 (y 2 (t)) + S 6 θ1 (t)] -S 5 θ2 (t), is practically ISS.

Proof: Note that

A = A 0 -GK + IF, where K = K 1 hK 2 K 3 K 5 and F = F 1 hF 2 F 3 F 5
contain the searched gains. Then with these designations, by applying Schur complement to the matrix Q, by multiplying it from the left and right by a positive definite matrix diag{P -1 , I 3n+p , I 3n+p , I 3n+p , I 3n+p , I 3n+p , I n }, using the identity

AP -1 = A 0 P -1 -GU + IW,
where W = FP -1 and U = K P -1 are decision variables, and introducing an auxiliary restriction

I 3n+p P -1 C CP -1 1 ρ Υ -1 ≥ 0,
we obtain Q ≤ 0, where we used the facts that ΓI = 0 and ΓG = B 1 . Two equalities given in ( 6) take the form

Σ = G + qh 2 B 1 (ΓA 0 P -1 -B 1 U) and Σ 2 = -qh 2 B 1 B 1 U 2 from 0 S 2 0 0 P -1 = -qh 2 B 1 B 1 0 K 2 0 0 P -1
, where Σ = SP -1 with S = S 1 hS 2 S 3 S 6 as before. Using Schur complement the inequality M M ≤ ρI s1+s2 can be represented as

ρI s1+s2 M M I 3n+p ≥ 0.
Finally, for the inequality 4 e -h h 2 I n ≥ αB B, note that B = h -1 (GK -IF)Γ , and this inequality takes the form

4 α e -h I n ≥ Γ(GK -IF) (GK -IF)Γ , which follows from 4 α e -h ∆ ≥ (GK -IF) (GK -IF).
Multiplying the latter by P -1 from the left and the right, we get:

4 α e -h P -1 ∆P -1 ≥ (GU -IW) (GU -IW),
and using again Schur complement, it can be transformed to

4 α e -h P -1 ∆P -1 U G -W I GU -IW I 3n+p ≥ 0.
As in [START_REF] Xu | Finite frequency h∞ control of singularly perturbed Euler-Lagrange systems: An artificial delay approach[END_REF], applying the inequality

P -1 4 α e -h ∆P -1 ≥ 2P -1 -α 4 e h ∆ -1 the latter inequality is satisfied provided that 2P -1 -α 4 e h ∆ -1 U G -W I GU -IW I 3n+p ≥ 0,
which is necessary to prove.

The last important observation is that for the algorithms (3), (4), (5) the variables K , F and S have an additional linear constraint (i.e., K 1 = -K 5 , F 1 = -F 5 and S 1 = -S 6 ), which is hard to formulate in terms of an LMI since K = UP , W = FP and S = ΣP , then a possible solution is to assume that the variable θ1 (t) in the algorithms [START_REF] Nekhoroshikh | On output-based accelerated stabilization of a chain of integrators: Implicit Lyapunov-Krasovskii functional approach[END_REF], ( 12), ( 13) enters with an independent gain.

Let us consider some results of application of the proposed robust adaptive output control.

V. APPLICATION TO A NONLINEAR PENDULUM

To illustrate the proposed approach, we consider an inverted pendulum stabilization problem, where the hardware setup used for experiments in this section has been previously reported in [START_REF] Aranovskiy | Differentiator-based velocity observer with sensor bias estimation: an inverted pendulum case study[END_REF]. The equipment and corresponding notation are shown in Fig. 1.

Define the state variable vector x := θ θ θr , where θ is the angle between the pendulum and the vertical, and θ r is the angle of the reaction wheel with respect to the pendulum. Note that the reaction wheel velocity θr is assumed to be available due to the equipment specifics. Derivations of the system dynamics and values of physical parameters can be found in [START_REF] Aranovskiy | Differentiator-based velocity observer with sensor bias estimation: an inverted pendulum case study[END_REF] and are omitted here; the resulting model is given by ẋ1

= x 2 , ẋ2 = a 1 sin(x 1 ) -b 1 u, ẋ3 = -a 1 sin(x 1 ) + b 2 u, (14)
where a 1 = 49.9, b 1 = 1.4, b 2 = 30.9, and u is the motor current considered as the control input. Due to physical reasons, the angle θ (the state x 1 ) is bounded as |x 1 | ≤ π 2 . The measurements are given by y 1 = x 1 + θ 1 and y 2 = x 3 , where θ 1 is the unknown constant bias of the pendulum position sensor. It is straightforward to verify that the model ( 14) can be written in the form [START_REF] Sastry | Adaptive Control: Stability, Convergence and Robustness[END_REF] with Ω(t) ≡ 0. The control goal is to drive the system to the origin and to estimate the bias θ 1 . In [START_REF] Aranovskiy | Differentiator-based velocity observer with sensor bias estimation: an inverted pendulum case study[END_REF] a nonlinear velocity observer for the state x 2 has been proposed and combined with the state-feedback control law; however, only local convergence has been shown. In this section, we apply the control law (3), (4). Assumption 1 is satisfied with Υ = diag[0.25, 0, 0]. The LMI ( 9) is feasible with h = 0.01 and K 1 = -102, K 2 = -1698, K 3 = -0.25, F 1 = 1, F 3 = 1.5 • 10 -4 , and K 4 = F 2 = F 4 = 0, thus the conditions of Remark 10 are verified.

Some simulation results for this setup were presented in the preliminary work [START_REF] Efimov | Adaptive stabilization by delay with biased measurements[END_REF]. In the experiment, the bias is θ 1 = 0.125 ≈ 7 • . The results of the experimental pendulum stabilization and θ 1 estimation with the control law (3), (4) are depicted in Fig. 2 for the estimated pendulum position y 1 -θ1 and the bias estimation θ1 . The experimental results for the reaction wheel velocity y 2 are depicted in Fig. 3, where the steady-state low-magnitude oscillations are attributed to the friction in the reaction wheel drive and compensation of external disturbances. The experimental results illustrate that the proposed delay-based control law stabilizes the system and allows for the bias estimation. The video of the experiment can be found here.

VI. CONCLUSIONS

Considering a Lipschitz nonlinear system, whose model contains external perturbation and uncertain parameters, while the measurements are available with a constant bias, the problem of robust output adaptive stabilization has been solved. Due to a severe uncertainty of the plant, the state reconstruction has been avoided by introducing artificial delays of the output in the feedback and adaptation algorithms. Applying the Lyapunov-Krasovskii approach, the conditions of practical ISS have been established, which are based on linear matrix inequalities. The efficacy of the proposed approach is demonstrated in experiments for an inertia wheel nonlinear pendulum. Extension of the proposed method to a more general class of systems is a direction of future research.

  II. PRELIMINARIES Denote by R the set of real numbers and R + = {s ∈ R : s ≥ 0}. For a Lebesgue measurable function of time d : [a, b] → R m , where -∞ ≤ a < b ≤ +∞, define the norm d [a,b) = ess sup t∈[a,b) |d(t)|, where | • | is the standard Euclidean norm in R m , then ||d|| ∞ = d [0,+∞) and the space of d with d [a,b) < +∞ (||d|| ∞ < +∞) we further denote as L m [a,b] (L m ∞ ). Denote by C n [a,b] , a, b ∈ R the Banach space of continuous functions φ : [a, b] → R n with the uniform norm φ [a,b] = sup a≤s≤b |φ(s)|; and by W 1,∞ [a,b] the Sobolev space of absolutely continuous functions φ : [a, b] → R n with the norm φ W = φ [a,b) +|| φ|| [a,b) < +∞, where φ(s) = ∂φ(s) ∂s is a Lebesgue measurable essentially bounded function, i.e. φ ∈ L n [a,b] . A continuous function σ : R + → R + belongs to class K if it is strictly increasing and σ(0) = 0; it belongs to class K ∞ if it is also radially unbounded. A continuous function β : R + × R + → R + belongs to class KL if β(•, r) ∈ K and β(r, •) is decreasing to zero for any fixed r > 0.

Figure 1 :

 1 Figure 1: The inverted pendulum hardware and corresponding notations, see [19].

  The corrected pendulum position y 1 -θ1 . The bias estimate θ1 and the true bias value θ 1 .

Figure 2 :

 2 Figure 2: Experimental stabilization of the inverted pendulum.

Figure 3 :

 3 Figure 3: Experimental stabilization of the inverted pendulum: the reaction wheel velocity y 2 .

  equals zero, and the term R (t)(αB B -4 e -h h 2 I n )R(t) is non-positive. Note that according to Assumption 1, φ (Cz(t))φ(Cz(t)) ≤ z (t)C ΥCz(t), and from M M ≤ ρI s1+s2 we get that φ (Cz(t))M Mφ(Cz(t)) ≤ ρz (t)C ΥCz(t).

)H (t)ΓDd(t) ≤ 0.5 θ 2 (t)H (t)ΓΓ H(t) θ2 (t) +0.5d (t)D Dd(t) = 0.5 θ 2 (t)H (t)H(t) θ2 (t) + 0.5d (t)D Dd(t). Due to the equalities imposed in (6), the expression in square brackets, which is multiplied from the left by θ 2 (t)Ω (t),

The preliminary version of this work[START_REF] Efimov | Adaptive stabilization by delay with biased measurements[END_REF] does not contain proofs and experiments, the main assumption is relaxed in this paper.

This work was partially supported by 111 project No. D17019 (China), by the Government of Russian Federation (Grant 08-08), by the Ministry of Science and Higher Education of Russian Federation, passport of goszadanie no. 2019-0898 and by Israel Science Foundation (grant No 673/19).


Alexander Yu Fedorchenko

William T T Taylor

Nuriddin N Sayfulloev

Samantha Brown

William Rendu

Andrei I Krivoshapkin

Katerina Douka

Svetlana V Shnaider

Early occupation of High Asia: New insights from the ornaments of the Oshhona site in the Pamir mountains

Keywords:

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Although Central Asia is renowned for its particularly rich cultural heritage, and its essential role in the movements of people, technology, goods, and ideas, from the Pleistocene to the modern era [START_REF] Harris | Investigating early agriculture in Central Asia: new research at Jeitun, Turkmenistan[END_REF][START_REF] Chaix | From social to genetic structures in central Asia[END_REF][START_REF] Kuzmina | The Prehistory of the Silk Road[END_REF][START_REF] Dennell | The Palaeolithic Settlement of Asia[END_REF][START_REF] Brunet | The Technique of Pressure Knapping in Central Asia: Innovation or Diffusion?[END_REF][START_REF] Rybin | Tools, beads, and migrations: Specific cultural traits in the Initial Upper Palaeolithic of Southern Siberia and Central Asia[END_REF][START_REF] Sharon | The Early Prehistory of Western and Central Asia[END_REF][START_REF] Pinhasi | Central Asia: Genetics and Archaeology[END_REF][START_REF] Kolobova | Developmental Continuity Between the Upper Palaeolithic and Mesolithic Industries of Western Central Asia[END_REF][START_REF] Bae | On the origin of modern humans: Asian perspectives[END_REF]Narasimhan et al., 2019;[START_REF] Zwyns | The Northern Route for Human dispersal in Central and Northeast Asia: New evidence from the site of Tolbor-16, Mongolia[END_REF], much of this area poses unique challenges to human occupation. The initial human settlement of the Central Asian territory -which ranges from the Eastern Caspian and Kopet Dag Mountains in the West to Tibet, Dzungaria and the Altai in the Eastduring the Late Pleistocene and Early Holocene required adaptation to high-altitude areas (2500-4500 m asl). Severe climatic and environmental challenges at high altitudes (including cold, hard winters, and limited oxygen) forced human populations to develop biological, economic and technologic adaptations [START_REF] Brantingham | A short chronology for the peopling of the Tibetan Plateau[END_REF][START_REF] Meyer | Permanent human occupation of the central Tibetan Plateau in the early Holocene[END_REF][START_REF] Slon | The genome of the offspring of a Neanderthal mother and a Denisovan father[END_REF][START_REF] Zhang | The earliest human occupation of the high-altitude Tibetan Plateau 40 thousand to 30 thousand years ago[END_REF][START_REF] Taylor | Early pastoral economies along the Ancient Silk Road: Biomolecular evidence from the Alay Valley, Kyrgyzstan[END_REF][START_REF] Taylor | Investigating Ancient Animal Economies and Exchange in Kyrgyzstan's Alay Valley[END_REF][START_REF] Shnaider | New insights into the Epipaleolithic of western Central Asia: The Tutkaulian complex[END_REF]. However, we know a little about the symbolic activities of early human societies in these environments. Personal ornaments, made of various organic and mineral raw materials, represent an essential element of cultural assemblages among the first occupants of highland Central and Inner Asia (Fig. 1). The first symbolic behaviour found across this broad region comes from Initial 50.0-30.0 ka cal BP [START_REF] Rybin | Tools, beads, and migrations: Specific cultural traits in the Initial Upper Palaeolithic of Southern Siberia and Central Asia[END_REF][START_REF] Douka | Age estimates for hominin fossils and the onset of the Upper Palaeolithic at Denisova Cave[END_REF]. Finds of ornaments from the Altai Mountains [START_REF] Derevianko | The earliest representations of symbolic behavior by Paleolithic humans in the Altai Mountains[END_REF][START_REF] Derevianko | Formation of the Upper Paleolithic Traditions in the Altai[END_REF][START_REF] Shunkov | The Early Upper Palaeolithic Personal Ornaments from the Southern Chamber of Denisova Cave. Problems of Archaeology, Ethnography, Anthropology of Siberia and Neighboring Territories[END_REF][START_REF] Fedorchenko | Early Upper Palaeolithic Serpentine ornaments from Ust-Karakol site, North-Western Altai[END_REF], Transbaikalia [START_REF] Lbova | Paleolithic of the northern zone of Western Transbaikalia[END_REF][START_REF] Tashak | Processing the ostrich eggs shell in the Upper Paleolithic of Transbaikalia[END_REF], Mongolia (Derevianko et al., 2007;[START_REF] Zwyns | The open-air site of Tolbor 16 (Northern Mongolia): Preliminary results and perspectives[END_REF][START_REF] Khatsenovich | Human and Struthio Asiaticus: One Page of Paleolithic Art in the Eastern Part of Central Asia[END_REF] and the Ordos [START_REF] Martí | The earliest evidence of coloured ornaments in China: The ochred ostrich eggshell beads from Shuidonggou Locality 2[END_REF][START_REF] Wei | An Early Instance of Upper Palaeolithic Personal Ornamentation from China: The Freshwater Shell Bead from Shuidonggou 2[END_REF][START_REF] Wei | A technological and morphological study of Late Paleolithic ostrich eggshell beads from Shuidonggou, North China[END_REF] show that ornament production was an important part of early human cultures across Inner Eurasia, which come from contexts ranging from 5 to 1500 m asl. The mass production of personal adornments was either an original cultural innovation or a response by local peoples to the arrival of a new population. Various types of ornaments worn in certain combinations may have been crucial markers of gender or age, tribal or clan affiliation, marital status, social standings, or levels of wealth (d'Errico et al., 2003;[START_REF] Kuhn | Body ornamentation as information technology: Towards an Understanding of the Significance of Early Beads[END_REF]. While a general picture of cultural and technological changes occurring during the Initial and Early Upper Paleolithic of Central Asia has been established based on flaked stone tools [START_REF] Kolobova | Developmental Continuity Between the Upper Palaeolithic and Mesolithic Industries of Western Central Asia[END_REF], no reliable evidence for the presence of personal ornament production is known for this areaparticularly for the earliest sites found at higher elevations of 2500 m asl and above. In the Early and Middle Holocene, various types of non-utilitarian objects made of bone, stone, and mollusc shells proliferated across lowland areas of Central Asia from the Aral-Caspian depression to the Ferghana Valley [START_REF] Okladnikov | The Jebel cave-site of the ancient culture of the Caspian tribes of Turkmenia[END_REF][START_REF] Gulyamov | Primitive culture and the emergence of irrigated agriculture in the lower reaches of Zarafshan[END_REF][START_REF] Markov | Dam Dam Cheshme 2 Rockshelter in Eastern Caspian[END_REF][START_REF] Vinogradov | Ancient hunters and fishermen of the Central Asian interfluve[END_REF][START_REF] Islamov | Stone Age Culture of Central Fergana[END_REF]Shnaider et al., 2018;Fedorchenko et al., 2018a). Ornaments made of organic or stone raw material from mountain areas in Central Asia are known only from the northern Tian Shan and Hissar ranges, and date to the terminal Late Pleistocene -Early Holocene (Fedorchenko et al., 2018b;[START_REF] Ozherelyev | Investigations of the Rakhat Upper Palaeolithic Multilayered site in Southeast Kazakhstan[END_REF][START_REF] Nokhrina | Personal Ornaments made of stone, bones and shells from the Karaungur cave (Southern Kazakhstan). Actual problems of Siberian Archaeology[END_REF][START_REF] Islamov | Machai cave[END_REF]. In the Soviet era, many ornaments and symbolic artefacts from mountains areas of Central Asia were identified from archaeological sites without radiocarbon dates or surface assemblages with problematic stratigraphy [START_REF] Vinogradov | Neolithic Ornaments from Didacna mollusk shells (by materials from excavation sites in Northern Turkmenistan)[END_REF][START_REF] Vinogradov | Ancient hunters and fishermen of the Central Asian interfluve[END_REF][START_REF] Gulyamov | Primitive culture and the emergence of irrigated agriculture in the lower reaches of Zarafshan[END_REF][START_REF] Vinogradov | Primeval Lyavlyakan. Stages of the most ancient settlement and development of Inner Kyzylkum[END_REF][START_REF] Islamov | Obishirian culture[END_REF][START_REF] Bizhanov | Mesolithic and Neolithic sites of the North-West Ustyurt[END_REF][START_REF] Itina | Rescue archaeological research in Horezm: results and prospects[END_REF][START_REF] Islamov | Stone Age Culture of Central Fergana[END_REF][START_REF] Korobkova | Mesolithic of Central Asia and Kazakhstan[END_REF]. The chronological and cultural attribution (Epipalaeolithic, Mesolithic or Early Neolithic) of personal adornments from this territory was usually determined using via relative dating based on accompanying stone tools or ceramics. Many Soviet publications reported only the presence or absence of ornaments and raw material type. As a result, traditions of manufacture, selection of raw materials, and use of these itemsalong with their complex social, cultural, and aesthetic functions, -have gone unnoticed or unstudied. Overall, early evidence of personal ornament production is still rare in Central Asia. Here we present a detailed analysis of the collection of bone ornaments from the site of Oshhona in the Pamir Mountains, Tajikistan, one of the oldest archaeological sites situated in the high mountains of Central Asia [START_REF] Ranov | Excavations of primitive communal system sites in the Eastern Pamir at 1960[END_REF][START_REF] Shnaider | Archaeological sites of the western part of Central Asia (Alai Valley and the Eastern Pamirs) in the context of the initial human settlement of highlands[END_REF]. The Oshhona personal adornments were recovered from secure archaeological contexts; a series of wellcorrelated radiocarbon dates have been generated for the site's cultural layers [START_REF] Ranov | Stone Age of the Afghan-Tajik Depression[END_REF]. The combination of absolute chronology and contextual information relating to the recovered ornaments, paired with the detailed study of material and manufacture technique, allows us to discuss the technology and production of symbolic objects by early human populations occupying the high mountain zones of Central Asia.

Regional settings

Situated in the heart of Central Asia, the Pamir mountains are located at the intersection between the Karakorum, Hindukush, Kunlun and Tian Shan mountains. The climate is arid, with short summers and long winters (minimum temperatures reaching -47 •C). The mountainous landscape is split by broad rivers and lake valleys, with elevations ranging from 3600 to 4200 m asl. Pamir vegetation is characterized by cryophytic alpine and subalpine meadows. Local populations in the Eastern Pamir consist mostly of ethnic Kyrgyz herders, who practice a traditional nomadic lifestyle and undertake (with their livestock, sheep, goat, and yak) several altitudinal migrations during the year. Wild fauna important to humans includes the Marco Polo sheep (Ovis ammon polii), Siberian ibex (Capra sibirica), Snow leopard (Uncia uncia), Eurasian lynx (Felix lynx), wolf (Canis lupus), and long-tailed marmot (Marmota caudata) [START_REF] Saidov | Mammals (Mammalia) of Pamir: conversation and management of resources. News of the Academy of Sciences of the Republic of Tajikistan[END_REF]. Systematic archaeological research in the Pamir mountains was conducted during the Soviet era by research teams led by V.A. Ranov and V.A. Zhukov [START_REF] Ranov | Excavations of primitive communal system sites in the Eastern Pamir at 1960[END_REF][START_REF] Zhukov | The works of the Markansuy archaeological expedition in 1976[END_REF][START_REF] Ranov | The Stone Age. In: History of the Gorno-Badakhshan Autonomous Region[END_REF]. In the eastern Pamir, these projects identified dozens of archaeological sites, most of which consisted of surface scatters. However, Ranov and Zhukov also identified two well-stratified localities, known as Oshhona and Istikskaya Cave [START_REF] Zhukov | The works of the Markansuy archaeological expedition in 1976[END_REF][START_REF] Ranov | Stone Age of Southern Tajikistan and the Pamir[END_REF]. Oshhonaanalysed hereis an open-air site located in the northern Pamir, within the Markansu valley. Vadim Ranov and his team discovered this site in 1957 and excavated an area of 563 m2 between 1957 and 1960. Archaeological remains were found at a depth of 0.2-1.5 m below the surface. Ranov identified four cultural layers, which he considered to belong to a single cultural complex. In the lithic assemblage, Ranov identified two knapping strategies. The first was based on pebble knapping, which was used to produce large flakes as blanks for scrapers. The second knapping strategy involved production the microblade by pressure knapping, wherein microblades were retouched and used as composite tools. The toolkit also contained endscrapers, awls, bifacial small arrows, notched bladelets, and backed bladelets. Previous researchers obtained a set of radiocarbon dates ranging between 11,202 and 10,512 cal BP for layer 2, and 8163-7690 cal BP and 8509-7880 cal BP for layer 3 (2-sigma or 95.4% probability, calibrated using IntCal13 in OxCal version 4.3). Researchers remain sceptical about the quality of dates from the second cultural layer, however, and tend to use only the later range of dates when describing the site [START_REF] Ranov | Stone Age of the Afghan-Tajik Depression[END_REF]. Since the original excavation, the personal ornaments from the site remained unstudied.

Materials and methods

Here we analyse the original collection of bone artefacts from layer 1 of the Oshhona site (Fig. 2). A total of six bone items occurs from this stratigraphic unit. These include a pendant with a perforation made of the wall of a tubular bone; a pendant with a hole made from a mammalian tooth; two elongated beads made of tubular small mammal bone; an elongated bead made of tubular bone of a carnivore; and a fragmented engraved bone.

Zooarchaeological study

Based on skeletal morphology, we identified each specimen to the most precise taxonomic level using comparative collections at the Russian Academy of Sciences-Siberian Branch in Novosibirsk, Russia. In cases where we could not make a species attribution, we used size classes [START_REF] Brain | The Hunter or the Hunted. An Introduction to African Cave Taphonomy[END_REF]. Identifiable specimens (including shaft fragments) were analysed for skeletal element, portion, and segment [START_REF] Gifford | A Computer Coding System for Archaeological Faunal Remains[END_REF]. Next, we conducted a microscopic observation of all bone to identify taphonomic modifications, including weathering, root etching, anthropogenic, and carnivore damage [START_REF] Olsen | Surface Modification on Bone: Trampling versus Butchery[END_REF][START_REF] Blumenschine | Blind Tests of Inter-Analyst Correspondence and Accuracy in the Identification of Cut Marks, Percussion Marks, and Carnivore Tooth Marks on Bone Surfaces[END_REF][START_REF] Behrensmeyer | Taphonomic and Ecologic Information from Bone Weathering[END_REF]d'Errico and Villa, 1997;[START_REF] Pickering | Experimental patterns of hammerstone percussion damage on bones: implications for inferences of carcass processing by humans[END_REF].

Zooarchaeology by Mass Spectrometry (ZooMS)

As most specimens could not be easily identified to taxon based on morphology, we conducted Zooarchaeology by Mass Spectrometry (ZooMS) analysis to taxonomically identify the bone artefacts at the Max Planck Institute for the Science of Human History in Jena, Germany. We followed protocols outlined by [START_REF] Welker | Ancient Proteins Resolve the Evolutionary History of Darwin's South American Ungulates[END_REF], allowing samples to demineralise in 0.5 M hydrochloric acid for one-two days after which they were rinsed back to a neutral pH using 50 mM ammonium bicarbonate. After rinsing, the sample was incubated at Thermo Scientific) at 37 •C for 18 h. Following digestion, we subjected samples to C18 cleanup (Pierce™ C18 Tips, Thermo Scientific), mixed with a matrix solution of α-cyano-4-hydroxycinnamic of 10 mg/mL in 50% acetonitrile (ACN)/0.1% trifluoroacetic acid (TFA) and allowed them to co-crystallise. Samples were then analysed using an Autoflex MALDI-TOF Bruker Ultraflex II (Bruker Daltonics, Bremen) Matrix Assisted Laser Desorption Ionization (MALDI) Time of Flight (ToF) Mass Spectrometer. The resulting mass spectra were analysed using mMass and screened for diagnostic markers using the FlexAnalysis software and compared against a reference library [START_REF] Buckley | Species identification by analysis of bone collagen using matrixassisted laser desorption/ionisation time-of-flight mass spectrometry[END_REF][START_REF] Welker | Palaeoproteomic Evidence Identifies Archaic Hominins Associated with the Châtelperronian at the Grotte Du Renne[END_REF]. Samples were also analysed alongside multiple blanks which all returned negative results, hence no crosscontamination was observed.

Technological and use-wear analysis

Using the technological approach and use-wear analysis, we reconstructed the technological context, sequence, and methods of production of artefacts [START_REF] Averbouh | Methodological specifics of the Techno-economic Analysis of worked bone and antler: mental refitting and method of application[END_REF]d'Errico et al., 2003;[START_REF] Broglio | Typological and Technological Study of Prehistoric Implements in Animal Hard Tissues[END_REF][START_REF] White | Systems of Personal Ornamentation in the Early Upper Palaeolithic: Methodological Challenges and New Observations[END_REF][START_REF] Khlopachev | Secrets of Ancient Carvers in Eastern Europe and Siberia: Processing Techniques of Mammoth Tusk and Reindeer Antler in the Stone Age[END_REF][START_REF] Goutas | From stone flaking to grinding: Three original Pavlovian antler tools from Moravia (Pavlov I, Czech Republic)[END_REF][START_REF] White | Early and Archaic Aurignacian Personal Ornaments from Isturitz Cave: Technological and Regional Perspectives[END_REF], following procedures developed by previous research [START_REF] Vanhaeren | Aurignacian ethno-linguistic geography of Europe revealed by personal ornaments[END_REF][START_REF] White | Systems of Personal Ornamentation in the Early Upper Palaeolithic: Methodological Challenges and New Observations[END_REF][START_REF] Wright | An Early Upper Palaeolithic decorated bone tubular rod from Pod Hradem Cave, Czech Republic[END_REF][START_REF] Heckel | Digital morphometric analysis of Upper Palaeolithic beads: Assessing artifact variability with user-friendly freeware[END_REF] and adapted to our region [START_REF] Shunkov | The Early Upper Palaeolithic Personal Ornaments from the Southern Chamber of Denisova Cave. Problems of Archaeology, Ethnography, Anthropology of Siberia and Neighboring Territories[END_REF]Fedorchenko et al., 2018a). First, we measured each artefact using electronic sliding callipers with a margin of error of 0.1 mm. We then conducted a use-wear analysis of the bone items to identify traces accumulated during manufacture and use at both low and high optical magnification, following established protocols [START_REF] Semenov | The development of technology in the Stone Age[END_REF][START_REF] Campana | A Natufian Shaft-Straightener from Mugharet El Wad, Israel: An Example of Wear-Pattern Analysis[END_REF][START_REF] Peltier | Micro-traseologie functionnelle sur l'os: quelques resultats experimentaux[END_REF][START_REF] Buc | Bone Tool Types and Microwear Patterns: Some Examples from the Pampa Region[END_REF]Legrand and Sid´era, 2007;[START_REF] Kononenko | Experimental and archaeological studies of use-wear and residues on obsidian artifacts from Papua New Guinea[END_REF][START_REF] Wright | An Early Upper Palaeolithic decorated bone tubular rod from Pod Hradem Cave, Czech Republic[END_REF]´Evora, 2015;[START_REF] Bradfield | Use-wear analysis of bone tools: a brief overview of four methodological approaches[END_REF][START_REF] Marreiros | Macro and Micro Evidences from the Past: The State of the Art of Archeological Use-Wear Studies[END_REF][START_REF] Stemp | Surface analysis of stone and bone tools[END_REF][START_REF] Dayet | Beads, pigments and early Holocene ornamental traditions at Bushman Rock Shelter, South Africa[END_REF][START_REF] Martisius | Time wears on: Assessing how bone wears using 3D surface texture analysis[END_REF]. Special attention was paid to the detection of the organic and inorganic remains on the artefact surfaces [START_REF] Wadley | The first residue analysis blind tests: results and lessons learnt[END_REF][START_REF] Rigaud | The way we wear makes the difference: residue analysis applied to Mesolithic personal ornaments from Hohlenstein-Stadel (Germany)[END_REF][START_REF] Martí | The earliest evidence of coloured ornaments in China: The ochred ostrich eggshell beads from Shuidonggou Locality 2[END_REF][START_REF] Velliky | Ochre and pigment use at Hohle Fels cave: Results of the first systematic review of ochre and ochre-related artefacts from the Upper Palaeolithic in Germany[END_REF]. We conducted a preliminary observation of every bone artefact using a stereomicroscope Altami SM0745-T with an external light source and with magnifications ranging from 7.5 × to 100 × . The main instrument used in a detailed examination of use-wear and manufacture tracessuch as scarring, rounding, striations, and abrasion polishwas a metallographic microscope Olympus BHM, using differential interference contrast (DIC) lenses with 40 × to 500 × magnifications. We recorded each artefact using a Canon EOS 7D digital SLR camera with lenses EF-S 60 mm f/2.8 Macro USM and a tripod with manual focusing. Micro-photography utilized a Canon EOS 7D and Olympus ВНМ optical system. For the creation of microphotographs focusing over the entire frame, we used Helicon Focus software, which is based on focus stacking technology.

Experimental data

Experimental criteria to identify bone artefact production techniques from the Final Pleistocene and Early Holocene have been productively applied to archaeological assemblages [START_REF] Semenov | The development of technology in the Stone Age[END_REF][START_REF] Olsen | Analytical approaches to the manufacture and use of bone artifacts in prehistory[END_REF][START_REF] Campana | Natufian and Protoneolithic Bone Tools. The Manufacture and Use of Bone Implements in the Zagros and the Levant[END_REF][START_REF] Lemoine | Use Wear on Bone and Antler Tools from the Mackenzie Delta, Northwest Territories[END_REF][START_REF] Gwinnett | A Brief History of Drills and Drilling[END_REF][START_REF] Korobkova | Stone Age bone tools (Diagnostics of Wear Traces on the Basis of Archaeological and Experimental Evidence)[END_REF][START_REF] Maigrot | Etude technologique et fonctionnelle de l'outillage en matières dures animales La station 4 de Chalain (Néolithique final[END_REF][START_REF] Pickering | Experimental patterns of hammerstone percussion damage on bones: implications for inferences of carcass processing by humans[END_REF]Legrand and Sid´era, 2007;[START_REF] Khlopachev | Secrets of Ancient Carvers in Eastern Europe and Siberia: Processing Techniques of Mammoth Tusk and Reindeer Antler in the Stone Age[END_REF][START_REF] Buc | Experimental series and use-wear in bone tools[END_REF]Averbouh and Petillon, 2011;´Alvarez et al., 2014;[START_REF] Abuhelaleh | An Experimental Study of Bone Artifacts from the Neolithic Site of Tell Abu Suwwan (PPNB-PN)[END_REF][START_REF] Gurova | Experimental Replication of Stone, Bone and Shell Beads from Early Neolithic Sites in Southeast Europe[END_REF][START_REF] Torres | A micro-wear analysis of Natufian gazelle phalanx beads from el-Wad Terrace, Mount Carmel, Israel[END_REF]. To understand the Oshhona material, we also used our experimental collection, produced to examine the manufacture and use-wear traces on artefacts made of mineral and osseous raw material. We employed various techniques and technologies for osseous raw material processing known from prehistoric Eurasia [START_REF] Fedorchenko | Performance test of Transverse burins from Northeast Asia[END_REF][START_REF] Fedorchenko | Pieces with Burin Spalls from Cultural Layer VI of Ushki-I (Kamchatka Peninsula)[END_REF][START_REF] Fedorchenko | Experimental Study of the Middle Paleolithic Technique from the Chagyrskaya Cave Assemblages in 2017[END_REF]Fedorchenko et al., , 2018a)). Our experimental program included modification of long bones of Rangifer tarandus, Cervus elaphus, Bos taurus taurus, and Ovis aries in dry and soaked condition. These experiments explored techniques for making longitudinal grooves in bone with stone burins, knapping and intentional fragmentation of bone raw material with hammerstones, wedges, and anvils, as well as planing/scraping of bone blanks using stone flakes, blades, and burins. We made an experimental grinding using grindstones made from sandstone and other abrasive raw material. We conducted perforation experiments using hand drilling, non-modified flint flakes with a narrow triangular shape, and a wooden bow drill with retouched micro-borer. We also relied on the reference collection at the Experimental-Traceological Laboratory of the Institute for the History of Material Culture RAS, Saint Petersburg. The conclusions of our experimental studies were used in the identification of the manufacturing techniques of the Oshhona bone artefacts.

Results

General characteristic of the faunal assemblage

The faunal assemblage of the site from V.A. Ranov excavation consists of 130 specimens (Table 1). The material is highly fragmented, and no complete elements were found. Based on the taphonomic study, most of this fragmentation occurred in antiquity while the bones still contained the grease and marrow. Less than 10% of the observed fractures were made on dry bones. Other taphonomic modifications are rare in the Oshhona assemblage, and limited weathering is present on only 30% of the remains. We do not observe carnivore marks and see root etching only on less than 10% of the remains. Of the 130 bone fragments, only 12 were taxonomically identifiable. These are all specimens of sheep or goat (Ovis/Capra), and include fragments of long bones (Femur = 2; Tibia = 2), metapodial (n = 4), scapula (n = 1), second phalange (n = 1) and tooth fragments (n = 2). In addition, 41 other remains were attributed to small-and medium-size ungulates (long bones = 17; flat bones = 13; vertebrae = 1). All these small/medium size ungulate remains could also belong to Ovis or Capra. In total, 19 specimens (14.6%) exhibit evidence of human activity. We identified cutmarks on five elements, including two femur shafts (likely related to defleshing) and two metapodials (disarticulation marks). Notches and bone percussion flakes attest to bone breakage, probably in order to recover marrow and grease.

Species identification of the blanks for personal ornaments

Although the process of ornament production removed most identifiable features of the bones necessary for species identification using traditional zooarchaeological techniques, three of the six specimens revealed high confidence taxonomic identifications based on collagen peptides using ZooMS. Two addition samples (samples 4 and 5) retain taxonomically essential markers but lack enough diagnostic markers to give high confidence assignments. Our results (Table 2) indicate the use of medium/large mammal species which may be wild or domestic (Ovis and Capra), small mammal prey species (rabbit/hare and Muridae, which may belong to a field mouse), and a predator species (cat), showing diverse exploitation of the mammalian fauna of the Pamir region.

Production process

The pendant made of Capra/Rangifer tubular bone is diamond-shaped (Table 2: sample 3; Fig. 3), with a straight profile and convex-concave cross-section following the original shape of the blank. The item is 22.1 mm long, 10.3 mm wide and from 1.3 to 2.5 mm thick (maximum dimensions). The pendant is made from a bone blank produced through fragmentation of a long bone through percussion. A few large chipping facets are noted at the bottom of the concave side of the artefact. Such traces are characteristic of the technique of direct percussion with a hammerstone [START_REF] Pickering | Experimental patterns of hammerstone percussion damage on bones: implications for inferences of carcass processing by humans[END_REF]. We note a traces of premeditated planing close to the perforation in the upper portion of the item's convex side. Evidence for planing is, however, difficult to distinguish due to overlapping usewear traces and, sometimes, root etching. The perforation has a round shape and biconical profile and is located in the upper portion of the artefact. The diameter of the hole is 3.5 mm. The interior surface of the hole shows concentric drilling striations arranged in even, parallel rows (Fig. 4). Upon marking the point intended for drilling on the concave side of the bone, a cone-shaped hole appears to have been formed by a stone tool with a narrow symmetrical point. The resulting perforation was drilled from the opposite side with the same tool. Morphological parameters of the perforation suggest the use of two-way drilling (Olsen, 1984: 153;[START_REF] Torres | A micro-wear analysis of Natufian gazelle phalanx beads from el-Wad Terrace, Mount Carmel, Israel[END_REF]. The shape of the hole suggests that drill rotated smoothly and freely around its axis, which could indicate the use of a bow drill [START_REF] Gwinnett | A Brief History of Drills and Drilling[END_REF]. Use-wear analysis of the pendant revealed use of this object in everyday life and wear. Under 40 × -100 × magnification, the convex side of the pendant close to the perforation shows micropolish, shallow multi-directional scratches and micro indentations, located mainly at protruding areas of the surface. On the concave side of the ornament, there are traces of rubbing and general use-wear resulting from contact with soft organic material [START_REF] Lemoine | Use Wear on Bone and Antler Tools from the Mackenzie Delta, Northwest Territories[END_REF]. The pendant's edges are rounded at the micro-level and show traces of lustre. At the top of the perforation, a localized area of smoothing and rubbing along with signs of overlapping concentric drilling striations is visible. These use-wear traces indicate a relatively firm attachment of the object to clothing with a thin thread [START_REF] Dayet | Beads, pigments and early Holocene ornamental traditions at Bushman Rock Shelter, South Africa[END_REF]. The pendant made from an Ovis/Cervidae/Saiga tooth (Table 2: sample 2; Fig. 5), is elongated and ovoid, with a straight profile and a subrectangular cross-section, which is due to the natural shape of the blank. The surfaces of the two lateral edges and one of the wide sides of the adornment are almost entirely missing due to lengthwise fragmentation. The object is 19.5 mm long, 7.3 mm wide and 2.8 mm thick (maximum dimensions). A round hole, biconical in the cross-section, was made in the root portion of the tooth. The diameter of the hole is 2.2 mm. Manufacture and use-wear traces on the artefact are partially destroyed due to exfoliation and desiccation-related fracturing. Traces of drilling preparation by planing or scraping, typical for pendants made of animal teeth (White and Normand, 2015: 145), are not visible on this artefact.

Morphological features of the perforation indicate the use of a two-way drilling technique using a small tool [START_REF] Gwinnett | A Brief History of Drills and Drilling[END_REF]. Micropolish on the upper part of the pendant and rub marks inside the hole, which overlap the concentric drilling striations, may suggest a relatively long and free movement of the pendant along the thread. Similar traces are considered as evidence of contact with the clothing or skin of a person who wore this ornament in everyday life [START_REF] Lemoine | Use Wear on Bone and Antler Tools from the Mackenzie Delta, Northwest Territories[END_REF]. The elongated bead made of tubular bone from a small rabbit or leporid (Table 2: sample 4; Fig. 6) has a narrow cylindrical shape, straight profile, and ovoid cross-section. These features follow the morphology of the original blank. The bead is 10.6 mm long, 3.3 mm wide and 2.7 mm thick (maximum dimensions). The diameter of the natural hole is 2 mm. At the initial stage of the elongated bead production, the epiphysis of the tubular bone was cut through deep, circular sawing and subsequently broken via flexion (Buc, 2011: 551) (Fig. 7: 1). The cutting surface is inclined at an angle of 80• to the cross axis of the item. The bead ends show four tentative cutmarks. The first is 2.9 mm long on one of the wide sides, and three other marks are 2.7 mm, 1.7 mm and 0.8 mm long on the opposite side. Analysis of manufacture traces suggests that the cutmarks were produced by a stone tool with reciprocal kinematics, straight profile, and symmetrical V-shaped working edge [START_REF] Wright | An Early Upper Palaeolithic decorated bone tubular rod from Pod Hradem Cave, Czech Republic[END_REF]. At the next stage, the item was carefully processed with fine-grained abrasives. Under 40 × -200 × magnification, the grinding traces appear as rows of elongated thin scratches oriented sub-parallel and perpendicular to the longitudinal axis of the artefact [START_REF] Bradfield | Use-wear analysis of bone tools: a brief overview of four methodological approaches[END_REF] (Fig. 8). Traces of grinding are overlapped and obscured by utilization wear across the surface of the decoration. Under 40 × -100 × magnification, the bead surfaces display visible traces of use-wear; micropolish is noted all over the rough microrelief; with rubbing signs and shallow micro indentations also visible (Fig. 7: 2). The surfaces of scratches and breakages at the bead ends are also smoothed and polished through prolonged use. This use-wear pattern suggests that the item was used together with other typologically similar artefacts as a part of a necklace. The elongated bead made of tubular bone from a сat (Felidae) (Table 2: sample 6; Fig. 9) is barrel-shaped and has a rounded cross-section and a straight profile. The decoration is 12.3 mm long. The width of the items varies from 5.5 mm in the medial part to 4.2 mm at the ends. The thickness of the bead varies similarly: from 3.4 mm to 4.3 mm at the ends to 5.3 mm in the medial portion. The diameter of the natural hole is 2.5 mm on one side and 3.3 mm on the opposite side. The initial stage of bead production was similar to that described above: the tubular bone epiphysis was cut or sawn with deep notches around the circumference of the bone, which was subsequently broken in the artisan's hands. The cutting surface was inclined at an angle of 50•-60• to the long axis of the object. Tentative cutmarks, 3.9 mm and 3.4 mm long, were noted on opposite sides at one of the bead's ends. The morphometric features of these traces suggest the use of a stone tool with a small symmetrical V-shaped working edge, such as an unretouched bladelet or flake. The exterior bead surfaces display visible use-wear traces: micropolish, rubbing traces, and shallow micro dents (Olsen, 1984: 168). The elongated bead, the same as the bead described above, might have been used as part of a necklace. The elongated bead made of a tubular bone from Muridae (Table 2: sample 5; Fig. 10) is cylinder-shaped, slightly expanding in diameter from one end to the other, with a straight profile and a flat-convex cross-sectional shape. The length of the artefact is 10.2 mm, the width is 6.3 mm, and the thickness is 5.2 mm (maximum dimensions). The diameter of the hole is 2.5 mm at one of the ends and 3.2 mm at the opposite end. Manufacture and usewear traces are poorly preserved due to natural deformation by exfoliation and pitting of the surface. The greater part of one of the broad bead surfaces has traces of exfoliating. The opposite surface and lateral faces of the item are less deformed. The general state of artefact preservation suggests the use of the same technological sequence as for the previous two ornaments. One of the bead tops was formed by circular sawing of the bone surface; the surfaces of the cutmarks are smoothed by planing and show use-wear micropolish. Sawing marks are not visible on the opposite end of the artefact; here the surface is levelled and ground; inside one micro-indentation, tiny particles of red ochre pigment are traced. We do not note the evidence of additional treatment inside the resulting natural hole. The foliate sheep (Ovis) bone fragment with traces of engraving (Table 2: sample 1; Fig. 11) shows a slightly curved profile and a flattened cross-section. Traces of fragmentation are discernible over much of the item's perimeter. The artefact is 55.6 mm long, 16.3 mm wide and from 1.1 to 2 mm thick (maximum dimensions). Five elongated engraved lines are made by a stone tool with a thin U-shaped working edge (Fig. 12). Sub-parallel traces of linear decoration are arranged diagonally to the artefact long axis. The lengths of the lines vary from 13.1 to 37.5 mm, the widths range from 0.1 to 0.2 mm, and the depth is 0.1 mm. Under 40 × -100 × magnification all grooves are relatively consistent in size and shape, which may suggest a smooth hand movement, and uniform tool specialised stone instrument like a small burin or engraver could have been used to create the ornament. We do not fix any other shreds of evidence of intentional manufacture on the artefact surfaces.

Age determination

We conducted new absolute dating of the Oshhona site assemblage using samples obtained from two bone fragments found in the archaeological collections stored at the Archaeological Department of the Institute of History, Archaeology and Ethnography (Dushanbe, Tajikistan). The samples were processed and dated at the AMS laboratory of the Centre for Cenozoic Geochronology, Institute of Archaeology and Ethnography SB RAS (Novosibirsk, Russia) and in the Centre for Isotope Research of Groningen University (Groningen, Netherlands) (Table 3). A sample from layer 1 gave a 14C Age of 6817 ± 104 BP (NSKA-1634) and calendar Age of 7922-7493 BP (2-sigma calibrated range using the INTCAL 13 calibration curve in OXCAL 4.3). The next sample obtained from layer 2 yielded an age of 6232 ± 105 BP (NSKA-1632) and 7415-6889 cal BP (2-sigma calibrated range). Finally, a third sample from the same layer, processed at the Centre for Isotope Research at the University of Groningen, gave a 14C Age of 6824 ± 18 BP (GrM-11930) and a calibrated age of 7685-7615 cal BP (2-sigma). Considering these new dates alongside the results of previous studies (Fig. 13), both layer 1 (where all the ornaments were found) and layer 2 appear to date to ca. 7650 BP, with the possibility of later occupation as well (that could also be attributable to radiocarbon contamination from specimen NSKA-1632). We suppose, the date 9530 ± 130 BP (RUL-280) is incorrect for layer 2; this sample was obtained from charcoal that may not directly reflect the age of cultural activity. Layers 3-4 may slightly predate the overlying layers, with previous dates falling between 8.5 and 7.7 ka cal BP.

Discussion

We discovered that inhabitants of the Oshhona site used osseous raw material from several local animal species to produce personal ornaments of various types. Archaeozoological and biomolecular analysis show that bone raw material belonging to a wide range of wild animal taxadeer, sheep, goat, cats, and rabbits/hares. The manufacture of the bone ornaments from Oshhona also employed several operational sequences. The technology of pendant production from mammalian teeth or wall of tubular bones was relatively simple using a short sequence: extraction of the tooth or selection of bones of suitable size/shape, preparation of the surface through planing or scraping, and finally two-way perforation of a rounded hole, likely using a simple device such as a bow drill. The manufacturing of elongated beads implied a more extended operation sequence. It included the following stages: removing the epiphysis of the tubular bone through deep circular cutting or sawing, breaking of the bone via flexion, and processing the surfaces with fine-grained abrasives. Use-wear patterns identified on these artefacts suggest that ornaments from Oshhona were used as the elements of a necklace, or sewn onto clothing. Comparison of our results with the archaeological record of the broader region of Central Asia suggests that occupants of mountain zones seem to have exploited local fauna while lowland occupants preferred other raw materials (Table 4). In the middle highlands of Central Asia, the earliest evidence of personal ornaments occurs from the multilayered site of Aigyrzhal-2, located in the Tian Shan mountains at an elevation of 2000 m asl [START_REF] Motuzaite Matuzeviciute | Ecology and subsistence at the Mesolithic and Bronze Age site of Aigyrzhal-2, Naryn Valley, Kyrgyzstan[END_REF]Fedorchenko et al., 2018b). At this site, a pendant with circular cutmarks made of a Cervus incisor was found in association with cultural layer 3 dated to 13.4-13.0 ka cal BP. A few pendants of Corbicula tibetensis shells with holes and red ochre have been reported at Rakhat multilayered site in the piedmonts of the Trans-Ili Alatau, one of the northern ranges of the Tian Shan [START_REF] Ozherelyev | Investigations of the Rakhat Upper Palaeolithic Multilayered site in Southeast Kazakhstan[END_REF]. This assemblage is preliminarily dated to the terminal Upper Palaeolithic. A unique set of personal ornaments also occur in association with the Early and Middle Holocene layers of the Karaungur Cave on the southern face of the Karatau mountain range (northwestern Tian Shan) [START_REF] Nokhrina | Personal Ornaments made of stone, bones and shells from the Karaungur cave (Southern Kazakhstan). Actual problems of Siberian Archaeology[END_REF]. The collection of bone items includes pendants made from teeth of small predators (Meles meles and Vulpes vulpes) and red deer (Cervus elaphus). This assemblage contains quadrilateral and round-shaped pendants with decorative motifs and red ochre, made of long bone fragments, as well as cylinder-shaped elongated beads decorated with linear incisions. Personal ornaments made from non-osseous raw material also revealed in Karaungur. These include an ovoid and patterned pendant made from slate, two cone-shaped elongated beads made of Corbicula ferganensis shell, and a pendant made of Dentallium sp. shell coloured with red ochre. A single ring-shaped bone pendant is known at Late Mesolithic assemblage of Machai Cave which is located in Baisuntau range and dated to 8.6-8.15 ka cal BP [START_REF] Islamov | Machai cave[END_REF]. More significant numbers of personal ornaments have been found in the assemblages of the low-mountain area of Central Asia, typically using stone rather than bone as raw materials for manufacture. The oldest evidence of symbolic activity for this territory occurs in the Fergana valley in the Early Holocene layers of Obishir-5 site (altitude 1700 m asl), dated to 10.8-8.2 ka cal BP [START_REF] Shnaider | New investigations of Epipaleolithic in western Central Asia: Obishir-5[END_REF]Fedorchenko et al., 2018a). The assemblage is made of soft stone and bone. The Obishir personal adornments include five artefacts made of talkite, serpentinite, and marble, produced through grinding and drilling. These are ovoid, subtriangular, and subrectangular pendants, a labret-like item, and a pendant blank. For the manufacture of stone ornaments, inhabitants of the Obishir-5 used raw material transported to the site over a distance of 4.5 km. The Early Holocene complex from this site also includes a pendant made of a Canis deciduous tooth with one biconical perforation (Islamov, 1980: 73). Other evidence of personal ornament production in the Fergana valley discovered through archaeological research is dated to the Mesolithic and Early Neolithic. This includes the sites of Uzunkul-1, -2 and -5; Dorazkul-1; Yangikadam-12, -16, -19, -25-27, -31, -32 and -35;Taipak-1, -9-12;Gurtepe;Madiar-1-3, -10a, and -13 sites (Islamov and Timofeev, 1986). For the manufacture of most non-utilitarian items from these sites, ancient inhabitants of Fergana valley used various types of soft stone. There are plain, rounded pendants made of small pebbles of marble-like rocks. These adornments have biconical perforations and are decorated through small carved notches at the edges. Small round beads are less common. A fragment of a complexshaped polished artefact, possibly a ring or a bracelet made of greenish-brown soft stone represents a unique find at the Madiar-2 site [Ibid: 100]. This artefact is curved and has a flattened cross-section. We should caution that the arid climate, typical of most of the landscape zones of Central Asia, may not be favourable to the preservation of animal bone ornaments in lower-lying areas. Nonetheless, osseous raw materials were undoubtedly known to the Epipalaeolithic and Early Neolithic inhabitants of Fergana, and consideration of these archaeological sites show that bone was widely used for the manufacture of non-utilitarian items. Finally, across the Aral-Caspian depression and Amu-Darya-Syr-Darya interfluve, personal ornaments appear to have been produced largely using shell and ornamental stone. On the south-eastern shores of the Caspian Sea and near the southwestern frontier of Central Asia series of pendants made of Didacna and Cerastoderma shells were found among the artefacts associated with the Epipalaeolithic assemblage of Ali Tappeh Cave [START_REF] Manca | Bone, shell tools and ornaments from the Epipalaeolithic site of Ali Tappeh, East of Alborz Range, Iran[END_REF]. Various types of Mesolithic and Neolithic personal ornaments were recovered from burials (Kaylu; Tumek-Kichidjik), in multilayer cave sites (Dam-Dan-Cheshme-1 and -2; Jebel), in settlements (Janbas-4; Lyavlyakan-7, -99 and -402; Darbazakyr-2 and Karrykyzy-1), in workshop sites (Kuba-Sengir) and in surface scatters [START_REF] Tolstov | Ancient Horezm. The experience of historical and archaeological research[END_REF][START_REF] Vinogradov | Neolithic Ornaments from Didacna mollusk shells (by materials from excavation sites in Northern Turkmenistan)[END_REF][START_REF] Vinogradov | Ancient hunters and fishermen of the Central Asian interfluve[END_REF][START_REF] Okladnikov | The Jebel cave-site of the ancient culture of the Caspian tribes of Turkmenia[END_REF][START_REF] Gulyamov | Primitive culture and the emergence of irrigated agriculture in the lower reaches of Zarafshan[END_REF][START_REF] Markov | Dam Dam Cheshme 2 Rockshelter in Eastern Caspian[END_REF][START_REF] Vinogradov | Primeval Lyavlyakan. Stages of the most ancient settlement and development of Inner Kyzylkum[END_REF][START_REF] Bizhanov | Mesolithic and Neolithic sites of the North-West Ustyurt[END_REF][START_REF] Itina | Rescue archaeological research in Horezm: results and prospects[END_REF][START_REF] Brunet | Pour une nouvelle étude de la culture néolithique de Kel'teminar[END_REF]. A large collection of rounded beads made of Didacna Eichwald mollusc shells (n > 900) occurs at the Kuba-Sengir archaeological site on the south-eastern Caspian Coast. The disc-shaped beads (n = 175) recovered from the burials at the Kayliu Cave produced important information for the reconstruction of the burial rite of the Early Holocene population of this region (Shnaider et al., 2018). At the Mesolithic -Early Neolithic Lyavlyakan sites of the Kyzylkum Desert, many truncated-conic beads, flat disc-shaped beads, rounded pendants made of green and light blue turquoise and white calcite, as well as flat beads of mollusc shells were identified [START_REF] Vinogradov | Primeval Lyavlyakan. Stages of the most ancient settlement and development of Inner Kyzylkum[END_REF].

While highland assemblages yield more animal bone in and Caspian sites exhibit a preference for shell, many sites located in transitional regions exhibit a diverse mix of all three material types. The Neolithic settlement of Jeitun, for example, is located at the junction between the Karakum desert and the foothill plain of the Kopet Dag mountains (8.3-8.0 ka cal BP) [START_REF] Masson | The settlement of Jeitun, the problem of the formation of the economy of production[END_REF][START_REF] Harris | Investigating early agriculture in Central Asia: new research at Jeitun, Turkmenistan[END_REF]. At this site, elongated beads and cylinder-shaped beads decorated with linear incisions were made from animal bone, as were pendants with biconical perforation. However, Jeitun's ornaments also include disc-shaped beads made of marble, turquoise, and other types of stone, flat beads, and pendants made of Didacna and Cypraeidae mollusc shells. At Jeitun, unique zoomorphic and anthropomorphic figurines with drilled holes were also used as personal ornaments, possibly functioning as amulets. Other evidence of personal ornament production from osseous raw material is known from the Tumek-Kichidjik Late Neolithic burial ground at Trans-Unguz Karakum Desert [START_REF] Vinogradov | Ancient hunters and fishermen of the Central Asian interfluve[END_REF]. This site includes 27 human burials, half of which yielded personal ornaments associated with red ochre. Some non-utilitarian items were found near the pelvis and femoral bones. These included small flat bone beads of the round and subrectangular shapes, Didacna mollusc shell round pendants with perforations, and flat beads made of soft stone. Ornaments of different types were also concentrated around the cranium: cylinder-shaped beads made of shells, pendants made of small predator fangs, and elongated beads made of bird tubular bones, some of which were decorated with linear incisions or deeper grooves. Large pendants with drilled holes at the ends made of boar fangs were found in two burials. These pendants represent remains of a peculiar necklace and were found between the neck and the abdomen. Although the symbolic traditions of high elevation occupants in the Pamir were poorly characterized before this research, our new results show the use of a diverse range of locally-available fauna for bone ornament production. Comparison with lowland areas of Central Asia reinforces a preference for locally-available materials in these regions. Mollusc shells and soft stone are the most popular in the Aral-Caspian depression, Amu-Darya-Syr-Darya interfluve and Ferghana valley. In contrast, sites of the Tian Shan region, Karakum desert and foothills of the Kopet Dag range exhibit a mix of faunal and stone raw materials.

Conclusion

The collection of personal bone ornaments from the Oshhona site provides new insight into the culture of the prehistoric populations of high altitudes in Central Asia. Our research shows that in the Middle Holocene period (prior to ca 7000 cal BP) in the Pamir mountains, a tradition of bone ornament production already existed in a developed form. Applying use-wear analysis and experimental data, we reconstructed the main techniques for the manufacturing of beads and pendants at the Oshhona site. According to the reconstruction, at least three operational sequences were employed by Oshhona inhabitants: manufacturing of barrel-shaped and cylinder-shaped elongated beads from tubular bones, creation of pendants with biconical perforation from the wall of tubular bones, and production of pendants with drilled holes from mammalian teeth. Production entailed the performance of several operations, beginning with fragmentation of the bone blanks by knapping or cutting, followed by shaping of the blanks by planing, drilling, and polishing. Although evidenced in our analysed assemblage, another operational sequencethe production of engraved bone items, -cannot be completely reconstructed at the moment, due to the fragmentation of available artefacts. Archaeozoological and biomolecular (ZooMS) analysis indicate that bone raw material belonging to a relatively wide range of wild animal taxadeer, sheep, goat, cat, and rabbit/harewere used to produce personal ornaments at Oshhona. This species diversity sits in contrast with the limited taxonomic diversity of the dietary assemblage at the site, which consisted primarily of sheep and goat remains. At the Oshhona site, the wide range of fauna remains used for the manufacture of the recovered ornaments indicates a non-exclusive use of specific raw materials. A cat bone, for example, was probably chosen deliberately for its cultural or spiritual significance, while other raw materials may have been selected based on practical considerations, such as availability or the size/shape of the desired skeletal elements. In total, the raw material and typological variability of the personal ornaments at Oshhona implies that specific preferences were used when choosing materials and for symbolic object manufacture. Ornaments and other non-utilitarian items made from rare raw material were often objects of prestige in ancient societies, and were gifted and exchanged during intergroup contacts [START_REF] Mayer | The exploitation of shells as beads in the Palaeolithic and Neolithic of the Levant[END_REF][START_REF] Wright | Stone Bead Technologies and Early Craft Specialization[END_REF]. Evidence of such practice is not apparent in the Oshhona archaeological record, where bone ornaments appear to have been used as personal items. We assume that the proliferation of symbolic activity across Central Asia in the Early and Middle Holocene might be linked to demographic increases or the appearance of new groups of people. This hypothesis is supported by an apparent increase in the number of archaeological sites and cultures in Central Asia following the end of the Pleistocene and the Last Glacial Maximum. Our research demonstrates that cultural adaptation to the diverse environments of Central Asia manifested in the selection of raw materials for personal ornaments, which appear consistently at Early Holocene sites from lowland territories to high mountain zones across the entire region. Comparison of the personal ornaments of Oshhona with collections from other areas dating to this period indicates that locally-available raw material was primarily selected for the production of non-utilitarian items, leading to regional differences in the use of bone, stone, and shell between high elevation, lowland, and Caspian-adjacent areas. Together, our results indicate the development of a robust tradition of animal-bone based ornament manufacture in highland Central Asia and the Pamir Mountains by ca. 7000 cal BP or before. Comparison of raw materials, manufacture technology, and typology of personal ornaments provide compelling evidence for cultural links between the Pamir mountains and the middle highlands of the Tian Shan. Although available anthropological and paleogenetic evidence is not yet numerous enough to assess the possibility of population movements linking these two regions, these results indicate a shared techno-cultural tradition or a common cultural adaptation, perhaps as a response to both available raw materials and emerging cultural preferences in montane environments during the first part of the Holocene.

Acknowledgements

We thank the organizers of the session and UISPP Congress 2018 for the invitation to participate in this special issue of Quaternary International. The analysis of personal ornaments and sampling for ZooMS analysis were supported by the Russian Foundation for Basic Research (RFBR) N• 18-09-40081 «Initial human colonization in the highlands of Western Central Asian (Pamir and Alay valley): cultural dynamics, chronology, palaeogeography» and the Max Planck Society. The radiocarbon dating and archaeozoological analysis were supported by the Russian Science foundation (RSF) N• 19-78-10053 «The emergence of food-producing economies in the high mountains of interior Central Asia». We also thank the anonymous reviewers for their comments and suggestions.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.