Zhang Liqin
email: liqinzhang@hnu.edu.cn

Member, IEEE Yougang Bian

Member, IEEE Anh-Tu Nguyen
email: nguyen.trananhtu@gmail.com

Liqin Zhang

Manjiang Hu
email: manjiangh@hnu.edu.cn

Senior Member, IEEE Hui Zhang
email: huizhang285@gmail.com

Rongjun Ding
email: dingrj@hnu.edu.cn

Channel-Level Event-Triggered Communication Scheme for Path Tracking Control of Autonomous Ground Vehicles With Distributed Sensors

Keywords: Autonomous ground vehicle, path tracking, decentralized control, event-triggered control, networked control system. I

In this paper, a channel-level event-triggered communication scheme is investigated for path tracking control of autonomous ground vehicles via an in-vehicle network to ensure path tracking performance while reducing network resource utilization. First, a path tracking system is established considering the effect of norm bounded uncertainty on lateral vehicle dynamics, and a state feedback path tracking controller is designed within the Takagi-Sugeno fuzzy framework. Next, a decentralized event-triggered communication scheme is adopted between the sensors and controller, which makes it possible to save communication resources at the channel level. Finally, the results in the CarSim-Simulink joint-simulation environment show that the proposed controller can ensure a reliable path tracking performance in both lateral offset and heading error. At the same time, compared with the simple time-triggered scheme, the proposed method can effectively reduce the usage of communication resources by more than 80%.

directly affects the driving safety and riding comfort [START_REF] Xu | Design, analysis, and experiments of preview path tracking control for autonomous vehicles[END_REF], [START_REF] Wang | Output-feedback triple-step coordinated control for path following of autonomous ground vehicles[END_REF], so it has always become a hot topic; see [START_REF] Cheng | Model-predictivecontrol-based path tracking controller of autonomous vehicle considering parametric uncertainties and velocity-varying[END_REF], [START_REF] Yang | Design and optimization of robust path tracking control for autonomous vehicles with fuzzy uncertainty[END_REF]- [START_REF] Milani | Smart autodriver algorithm for real-time autonomous vehicle trajectory control[END_REF] and the references therein.

Different path tracking strategies have been proposed in existing studies to help AGVs track pre-defined reference trajectories smoothly and accurately, e.g., game theory-based control [START_REF] Hu | Cooperative-game-theoretic optimal robust path tracking control for autonomous vehicles[END_REF], [START_REF] An | Game theory-based control strategy for trajectory following of four-wheel independently actuated autonomous vehicles[END_REF], sliding mode control [START_REF] Milani | Smart autodriver algorithm for real-time autonomous vehicle trajectory control[END_REF], [START_REF] Chen | Path following control of autonomous four-wheel-independent-drive electric vehicles via secondorder sliding mode and nonlinear disturbance observer techniques[END_REF], model predictive control (MPC) [START_REF] Cheng | Model-predictivecontrol-based path tracking controller of autonomous vehicle considering parametric uncertainties and velocity-varying[END_REF], [START_REF] Chen | Design and experimental evaluation of an efficient MPC-based lateral motion controller considering path preview for autonomous vehicles[END_REF]- [START_REF] Ji | Path planning and tracking for vehicle collision avoidance based on model predictive control with multiconstraints[END_REF], and fuzzy logic control [START_REF] Yang | Design and optimization of robust path tracking control for autonomous vehicles with fuzzy uncertainty[END_REF], [START_REF] Nguyen | Fuzzy static output feedback control for path following of autonomous vehicles with transient performance improvements[END_REF], [START_REF] Zhang | A novel fuzzy observer-based steering control approach for path tracking in autonomous vehicles[END_REF]. Most of these works are based on models, either kinematic or dynamic, and the accuracy of the model is extremely crucial to controller performance. Nevertheless, since vehicle systems are complex and nonlinear [START_REF] Zhang | A novel manoeuvre stability controller based on vehicle state prediction and intellectual braking torque distribution[END_REF], there are inevitable mismatches between the model and the real one. For example, linear tire cornering stiffness is often used in vehicle models [START_REF] Xu | Design, analysis, and experiments of preview path tracking control for autonomous vehicles[END_REF], but its actual value has obvious nonlinear characteristics [START_REF] Hu | Cooperative-game-theoretic optimal robust path tracking control for autonomous vehicles[END_REF], [START_REF] Zhang | A novel robust event-triggered fault tolerant automatic steering control approach of autonomous land vehicles under in-vehicle network delay[END_REF], [START_REF] Li | Robust gain-scheduling static output-feedback H∞ control of vehicle lateral stability with heuristic approach[END_REF]. Moreover, there are some time-varying parameters, e.g., vehicle mass [START_REF] Zhang | A novel fuzzy observer-based steering control approach for path tracking in autonomous vehicles[END_REF], [START_REF] Zhu | Parameterspace based robust gain-scheduling design of automated vehicle lateral control[END_REF], and longitudinal speed [START_REF] Cheng | Model-predictivecontrol-based path tracking controller of autonomous vehicle considering parametric uncertainties and velocity-varying[END_REF], [START_REF] Mata | Robust tube-based model predictive control for lateral path tracking[END_REF], [START_REF] Corno | An LPV approach to autonomous vehicle path tracking in the presence of steering actuation nonlinearities[END_REF], [START_REF] Li | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication[END_REF]. All these uncertainties may introduce uncontrollable conditions for path tracking control [START_REF] Yang | Design and optimization of robust path tracking control for autonomous vehicles with fuzzy uncertainty[END_REF], and make it a tough task [START_REF] Yang | Path tracking control for underactuated vehicles with matched-mismatched uncertainties: An uncertainty decomposition based constraint-following approach[END_REF]. To deal with the aforementioned uncertainties, the Takagi-Sugeno (T-S) fuzzy method [START_REF] Nguyen | Fuzzy static output feedback control for path following of autonomous vehicles with transient performance improvements[END_REF], [START_REF] Zhang | A novel fuzzy observer-based steering control approach for path tracking in autonomous vehicles[END_REF], [START_REF] Zhu | Parameterspace based robust gain-scheduling design of automated vehicle lateral control[END_REF], has been proved to be an effective way. It is worth noting that the fuzzy system and controller studied above usually share the same membership function and have limited flexibility.

As a typical decentralized system, the vehicle control system has different types of sensors, controllers, and actuators that are scattered throughout the vehicle due to functional requirements. Known as network nodes [START_REF] Natale | Moving from federated to integrated architectures in automotive: The role of standards, methods and tools[END_REF], these sensors, controllers, and actuators are physically connected via a controller area network (CAN) to form a networked control system (NCS) [START_REF] Li | An improved event-triggered communication mechanism and L∞ control co-design for network control systems[END_REF], [START_REF] Yue | A delay system method for designing event-triggered controllers of networked control systems[END_REF], resulting in a lighter wiring harness [START_REF] Gao | Distributed active disturbance rejection control for ackermann steering of a four-in-wheel motor drive vehicle with deception attacks on controller area networks[END_REF]. As part of the network, different nodes collect information about the vehicle state, and share the information with each other via the network. Nevertheless, in response to recent advances in vehicle safety and performance, including autonomous driving, more and more information must be transmitted over the in-vehicle network, exacerbating the occupancy of invehicle network resources [START_REF] Ahmad | Decentralized dynamic eventtriggered communication and active suspension control of in-wheel motor driven electric vehicles with dynamic damping[END_REF]. Unfortunately, a high network bandwidth occupation will lead to problems such as network delay and packet loss, which are random and cannot be ignored [START_REF] Qi | Tuning of digital PID controllers using particle swarm optimization algorithm for a CAN-based DC motor subject to stochastic delays[END_REF]. To this end, the delay and data dropout problem of CAN was modeled in [START_REF] Wang | Robust H∞ path following control for autonomous ground vehicles with delay and data dropout[END_REF], and the path tracking problem of AGVs under random network delay was investigated in [START_REF] Shi | Road-curvature-range-dependent path following controller design for autonomous ground vehicles subject to stochastic delays[END_REF], [START_REF] Luan | Trajectory tracking control of autonomous vehicle with random network delay[END_REF]. Further, to proactively solve the issue of occupancy of limited network resources, an event-triggered communication mechanism was proposed as an alternative mechanism to remove the limitations of the traditional periodic one, see [START_REF] Peng | A survey on recent advances in event-triggered communication and control[END_REF] and its references for details. The existing literature has yielded some interesting results for the event-triggered control problem of CAN-based in-vehicle network systems, e.g., active suspension systems [START_REF] Ahmad | Decentralized dynamic eventtriggered communication and active suspension control of in-wheel motor driven electric vehicles with dynamic damping[END_REF], [START_REF] Ge | Dynamic event-triggered scheduling and control for vehicle active suspension over controller area network[END_REF], path following systems [START_REF] Zhang | A novel robust event-triggered fault tolerant automatic steering control approach of autonomous land vehicles under in-vehicle network delay[END_REF], [START_REF] Li | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication[END_REF], and lateral dynamics control systems [START_REF] Li | Adaptive-event-triggerbased fuzzy nonlinear lateral dynamic control for autonomous electric vehicles under insecure communication networks[END_REF]. However, most of the studies above rely on a centralized event-triggered communication mechanism (CETCM), which requires the event generator to obtain all state information simultaneously. Consequently, for distributed sensor systems like vehicles, the CETCM is unsuitable due to the difficulty of measuring all state information with a single sensor simultaneously, or the cost is too high [START_REF] Ahmad | Decentralized dynamic eventtriggered communication and active suspension control of in-wheel motor driven electric vehicles with dynamic damping[END_REF], [START_REF] Zhang | Observer-based decentralized event-triggered H∞ control for networked systems[END_REF], [START_REF] Tallapragada | Decentralized event-triggering for control of nonlinear systems[END_REF]. The decentralized event-triggered communication mechanism (DETCM) is a more feasible solution [START_REF] Tallapragada | Decentralized event-triggering for control of nonlinear systems[END_REF], [START_REF] Zhao | Decentralized dynamic event-triggered H∞ control for nonlinear systems with unreliable communication channel and limited bandwidth[END_REF]. In this case, each individual sensor determines whether to broadcast and transmit data to the network according to only locally available information, which can effectively save network bandwidth resources. In addition, it should be pointed out that the controller and actuators are usually directly connected point-to-point and the computational resources of the controller are much more affluent compared to the limited network resources. Therefore, a time-triggered communication mechanism (TTCM) would be more appropriate.

Based on the above analysis, this paper discusses the path tracking control problem of AGVs with distributed sensors via a decentralized event-triggered communication scheme. As shown in Fig. 1, there is a communication network between the sensors and controller, which in turn is directly connected to the actuator through a zero-order-holder (ZOH). Different system states are sampled by corresponding sensors at a fixed time interval, and the sampled state values that meet the triggering condition are sent to the controller through a CAN bus with DETCM. After receiving and storing the sampled state values sent by the sensors, the controller periodically calculates the control input according to these values with TTCM. With the co-design of the path tracking control and decentralized eventtriggered communication scheme, network resources are saved while guaranteeing satisfactory path tracking performance.

The main contributions of this paper are summarized as follows.

1) By taking into account the distribution nature of state sensing and communication in CAN-based vehicle control systems, a DETCM is proposed for path tracking control of AGVs. Compared with [START_REF] Zhang | A novel robust event-triggered fault tolerant automatic steering control approach of autonomous land vehicles under in-vehicle network delay[END_REF], [START_REF] Li | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication[END_REF], this method removes the assumption of synchronous state component sensing, and thus enables event-triggered communication in each measuring channel for further communication resource saving in CAN.

2) A general T-S fuzzy lateral dynamics model is established

considering the influence of norm bounded uncertainties in, e.g., vehicle mass, longitudinal speed, and tire cornering stiffness, and an imperfect premise matching (IPM) method is adopted to design the path tracking controller.

Compared with [START_REF] Zhang | A novel robust event-triggered fault tolerant automatic steering control approach of autonomous land vehicles under in-vehicle network delay[END_REF], [START_REF] Li | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication[END_REF], the controller does not require the same premise variables as the T-S fuzzy system, allowing greater flexibility in design. 3) By analyzing typical vehicle test cycles and CAN-induced delay characteristics, an algorithm for determining the membership function parameter is proposed to ensure that the membership function design conditions always hold. Unlike [START_REF] Lam | Stability analysis and performance design for fuzzy-model-based control system under imperfect premise matching[END_REF], [START_REF] Peng | Observer-based Non-PDC control for networked T-S fuzzy systems with an event-triggered communication[END_REF], the membership function parameter is directly given, which results in a lack of clear physical meaning. 4) The effectiveness of the proposed path tracking controller with the decentralized event-triggered communication scheme is validated in a high-fidelity CarSim-Simulink joint-simulation environment. The paper is organized as follows. Section II formulates the problem. Section III presents the main results. Simulation results are given in Section IV. Finally, Section V concludes the paper.

Notation: The integers fields, positive integers fields, ndimensional Euclidean space, and n × m real matrix are denoted by N, N + , R n , and R n×m , respectively. The superscript 'T' ('-1') is used to represent the transpose (inverse) of a matrix. The space of square-integrable vector functions over [0, ∞) is denoted by L 2 [0, ∞), and for

w(t) ∈ L 2 [0, ∞), its 2- norm is denoted by w(t) 2 = ∞ t=0 |w(t)| 2 dt.
The symbol I (0) represents the identity (zero) matrix of appropriate size. For any square matrix X, X>0 (X<0) indicates a positive (negative) definite matrix. The symbol ' * ' stands for matrix blocks that can be deduced by symmetry. The symbol diag(. . .) stands for a block diagonal matrix. Matrices throughout the paper, if not explicitly stated, are assumed to have compatible dimensions.

II. SYSTEM MODELING AND PROBLEM FORMULATION

A. Lateral vehicle dynamics with parameter uncertainties and path tracking model

A common two-degree-of-freedom vehicle model, as shown in the upper left corner of Fig. 1, is used for path tracking controller design in this subsection. Assuming that the tire slip angle is small and the vehicle's longitudinal speed v x is constant, the lateral vehicle dynamics can be expressed in the following form

vy ṙ =   -2(C f +Cr) mvx 2(bCr-aC f ) mvx -v x 2(bCr-aC f ) Izvx -2(a 2 C f +b 2 Cr) Izvx   v y r + 2C f m 2aC f Iz δ, (1)
where the symbols are given in Table I.

Nevertheless, the cornering stiffness of a tire is not constant due to the nonlinear relationship between the tire lateral force and its slip angle [START_REF] Wang | Robust H∞ path following control for autonomous ground vehicles with delay and data dropout[END_REF]. Not only that, but different driving conditions will affect it, including tire slip angle, temperature, and many other factors [START_REF] Zhang | A novel fuzzy observer-based steering control approach for path tracking in autonomous vehicles[END_REF]. Therefore, it is necessary to consider the change of the tire cornering stiffness. By introducing the uncertain cornering stiffness terms ∆C f and ∆C r , the tire cornering stiffness in (1) can be further expressed as [START_REF] Zhang | Robust gain-scheduling energy-topeak control of vehicle lateral dynamics stabilisation[END_REF]

C i = C 0i + ∆C i ζ i (t), i ∈ {f, r} , (2)
∆C i = C i -C i /2.
Denote by e y the lateral offset from the center of gravity (CG) to the closest point on the desired path s, and by e ψ the heading error between the desired heading angle ψ d and the actual one ψ, similar to [START_REF] Shi | Road-curvature-range-dependent path following controller design for autonomous ground vehicles subject to stochastic delays[END_REF], then the path tracking model of the AGV can be expressed as

ėy = v x e ψ -v y , ėψ = v x ρ(s) -r, (3)
where ρ(s) is the road curvature along the desired path. In general, the lateral offset e y and heading error e ψ need to be as small as possible. Denote x(t) [e y , e ψ , v y , r] T as the state vector, u(t) δ as the control input, and ω(t) ρ(s) as the external disturbance. By using (1)-(3), the system model can be expressed in the following matrix form

ẋ(t) =Ax(t) + Bu(t) + B 1 ω(t) = (A 0 + ∆A) x(t) + (B 0 + ∆B) u(t) + B 1 ω(t) (4)
where

A 0 =      0 v x 1 0 0 0 0 1 0 0 -2(C f +Cr) mvx 2(bCr-aC f ) mvx -v x 0 0 2(bCr-aC f ) Izvx -2(a 2 C f +b 2 Cr) Izvx      , B 0 = 0 0 2C f m 2aC f Iz T , and
B 1 = 0 -v x 0 0 T .
In addition, the matrices ∆A and ∆B are norm-bounded uncertainties caused by the uncertain cornering stiffness ∆C f and ∆C r . According to (1) and (2), we have

∆A ∆B = EF G 1 G 2 , (5)
where

E = 0 0 -2∆Cr mvx 2b∆Cr Izvx 0 0 -2∆C f mvx -2a∆C f Izvx T , G 1 = 0 0 1 -b 0 0 1 a , F (t) = diag ζ r (t), ζ f (t) , and G 2 = 0 -v x T .
Remark 1. To reduce the complexity of the problem, it is reasonable to assume that the unknown time-varying parameters ζ f (t) = ζ r (t) = ζ(t) because the road conditions are usually uniform to both the front and rear wheels [START_REF] Wang | Robust H∞ path following control for autonomous ground vehicles with delay and data dropout[END_REF]. In this case, the matrix F (t) can be written as

F (t) = ζ(t)•diag(1, 1).

B. T-S fuzzification of the vehicle model

It is noted that the longitudinal vehicle velocity generally varies due to the exterior driving environment or other reasons in practical applications. With the velocity changing, system (4) will be time-varying due to the existence of the term v x . In addition, vehicle mass m and yaw inertia I z vary with the number of passengers or vehicle load, which also causes system time-varying. In this subsection, the T-S fuzzy modeling approach will be adopted to deal with the timevarying problem caused by the above parameter changes [START_REF] Li | Polytopic LPV approaches for intelligent automotive systems: State of the art and future challenges[END_REF].

Without loss of generality, the varying longitudinal vehicle

velocity v x is bounded in the range [v x , v x ] with v x , v x > 0,
and the vehicle mass m varies in the interval

[m, m]. Define σ 1 (t) v x , σ 2 (t)
1 vx , and σ 3 (t)

1 m as the premise variables, the uncertain term can be presented as follows

σ k (t) = H k,1 (σ k (t))σ k + H k,2 (σ k (t))σ k , k ∈ {1, 2, 3} , (6)
where the overline • and the underline • denote the maximum and minimum values of •, respectively. The membership functions H k,1 (σ k (t)) and H k,2 (σ k (t)) in ( 6) satisfy the following relationship

H k,1 (σ k (t)) = σ k -σ k (t) σ k -σ k , H k,2 (σ k (t)) = σ k (t) -σ k σ k -σ k . (7)
It is easy to find that

H k,1 (σ k (t)) + H k,2 (σ k (t)) ≡ 1.
Combining the above analysis, system (4) with time-varying parameter σ k (t) can be formulated by the following IF-THEN rules based on the T-S fuzzy modeling method [START_REF] Wang | Fuzzy control systems design and analysis: A linear matrix inequality approach[END_REF]:

Model Rule j: IF σ 1 (t) is H 1, (σ 1 (t)), σ 2 (t) is H 2, (σ 2 (t)), and σ 3 (t) is H 3, (σ 3 (t)), THEN ẋ(t) =A j (σ 1 (t), σ 2 (t), σ 3 (t)) + B j (σ 3 (t)) u(t) + B 1j (σ 1 (t)) ω(t) , (8)
where ∈ {1, 2} , j ∈ {1, 2, . . . , 8}, and the matrices A j , B j , and B 1j can be obtained by replacing σ k (t) with the maximum value σ k or the minimum value σ k in system model ( 4), respectively.

For convenience, fuzzy system ( 8) is further expressed in the following concise form

ẋ(t) = 8 j=1 η j (σ(t)) [A j x(t) + B j u(t) + B 1j ω(t)] (9)
where the membership factor η j (σ(t)) is nonnegative and 8 j=1 η j (σ(t)) = 1. For brevity, denote η j η j (σ(t)), then it can be specifically defined as follows

η 1 = H 1,1 (σ 1 (t))H 2,1 (σ 2 (t))H 3,1 (σ 3 (t)) η 2 = H 1,1 (σ 1 (t))H 2,1 (σ 2 (t))H 3,2 (σ 3 (t)) . . . . . . . . . η 8 = H 1,2 (σ 1 (t))H 2,2 (σ 2 (t))H 3,2 (σ 3 (t)) . ( 10
)
Remark 2. The changes in vehicle mass m and yaw inertia I z often exist at the same time. To reduce the complexity of the T-S fuzzy system, in this study, we assume that the value of I z changes simultaneously with m, that is, when the vehicle mass is at its maximum value, the yaw inertia also takes the maximum value, and vice versa.

C. Decentralized event-triggered communication mechanism design

In this subsection, a DETCM is proposed to address the limitation of the centralized one by designing individual triggering conditions for each sensor. Specifically, each system state component x n (t), n ∈ N + , is measured by sensing unit Sn at a constant sampling interval h, and the sampled system state at time l n h is denoted as x n (l n h), l n ∈ N. And then, event generator Gn determines whether to broadcast and transmit the current sampled data x n (l n h), through a unique frame ID, by judging whether it meets the triggering condition. If it does, record the current sampled data as x n (t m n h), where t m n h is the event-triggering instant of Gn, t m n ∈ N.

Remark 3. DETCM described above is a general mechanism for distributed sensing systems. Specific to this study, since the lateral offset e y and heading error e ψ are generated by the same network node, it is natural to encapsulate them in the same data frame and send together. In particular, as depicted in Fig. 1, the event generator G1 makes trigger judgments according to the sampling values of the two measurement channels, i.e., c 1 and c 2 , of the sensing unit S1. A CAN data frame, containing the current e y and e ψ , will be sent to the network if the trigger condition is met; otherwise, it will not. As a result, the timestamps of their samples are the same in this case, which we denote by t m1 1 in Fig. 1. Similarly, in the following, we will provide a general derivation of distributed sensing systems, based on which we will specify the path tracking problem studied in this study.

A memory stack is allocated for each state component, and once a frame update for Sn is received, its value is pushed to the top of the corresponding stack, which is periodically read by the controller. According to the CAN communication protocol, e.g., ISO 11898, only one network node can send a frame at the same time. In addition, the priority of sending is determined by the ID of the frame. The smaller the ID, the higher the priority. For those frames that fail to compete, they will be waiting for the frames with higher priority to be sent before sending. Therefore, there will be an inevitable time delay.

Considering the limited bandwidth of the CAN network, a DETCM is introduced to reduce the communication burden without sacrificing too much system performance. The event generator Gn is employed to determine the next triggering instant for sensor Sn with the following triggering rule

t m+1 n = t m n +min l n e T n (t m n h + l n h) Φ n e n (t m n h + l n h) ≥ n (t)x T n (t m n h) Φ n x n (t m n h) (11
h + l n h) = x n (t m n h) -x n (t m n h + l n h). (12)
The weighting matrix Φ n is a positive definite matrix of appropriate size to be designed. Considering all states of the system, define an aggregated weight matrix Φ as

Φ = diag(Φ 1 , Φ 2 , . . . , Φ n ). ( 13
)
Remark 4. The positive weight matrix Φ to be designed in ( 13) is a block diagonal matrix, which is the main difference between the DETCM and the centralized ones. In this case, special treatment is required in the solution process, which will be covered later in Remark 10. Specific to system (4), there are n equals 3, Φ 1 ∈ R 2 , Φ 2 and Φ 3 are positive constants.

In addition, the event-triggering threshold n (t) is calculated with the following update rule

˙ n (t) = -1 n (t) -1 n (t)-0 e T n (t m n h+l n h) Φ n e n (t m n h+l n h), (14)
where 0 > 0 is a given initial scalar parameter. Remark 5. Each event generator determines whether or not to transmit the current sampled data based solely on locally available information, which makes it possible to improve the communication bandwidth occupation from the channel level. When condition [START_REF] Chen | Path following control of autonomous four-wheel-independent-drive electric vehicles via secondorder sliding mode and nonlinear disturbance observer techniques[END_REF] is satisfied, the sensor will apply for data transmission. At this time, if the bus is free and there is no higher-priority frame competition, the sampled status data will be broadcast. Otherwise, it will wait until the higherpriority frame is sent and the bus is free before sending. When condition [START_REF] Chen | Path following control of autonomous four-wheel-independent-drive electric vehicles via secondorder sliding mode and nonlinear disturbance observer techniques[END_REF] is not met, the current sampled data will be discarded directly. Therefore, the number of sample data transfers can be reduced.

D. Controller design of the networked control system

The broadcast feature of CAN communication ensures that once a network node sends a message to the bus, the other network nodes will immediately start receiving it. However, it will take some time for the message to be transmitted over the network. For example, the theoretical transmission time is approximately 216us for a 108-bit standard data frame on a high-speed CAN network with a communication speed of 500kbps. Furthermore, due to bus occupancy and the necessary read/write operations of the microprogrammed control unit [START_REF] Qi | Tuning of digital PID controllers using particle swarm optimization algorithm for a CAN-based DC motor subject to stochastic delays[END_REF], the complete receipt of the message by a specific network node tends to lag further. Therefore, there is inevitably a network-induced delay in the process of network information transmission, as shown in Fig. 2 [START_REF] Yue | A delay system method for designing event-triggered controllers of networked control systems[END_REF], which will deteriorate the control performance of the NCS.

Without losing generality, define the moment when the controller receives the message sent by sensor Sn as

T m n = t m n h + τ m n ,
where τ m n is the network-induced delay. Therefore, the system state received by the controller can be expressed as

xn (t n ) = x n (t m n h), t n ∈ Ω [t m n h + τ m n , t m+1 n h + τ m+1 n ), (15)
where τ m n (m ∈ N + ) is the norm bounded delay that satisfies τ ≤ τ m n ≤ τ . Remark 6. For the same electrical environment, to simplify the problem, we consider that the upper and lower bounds of network-induced delay for different network nodes are the same.

Further, similar to [START_REF] Yue | A delay system method for designing event-triggered controllers of networked control systems[END_REF], we consider the following two cases for time interval Ω.

Case 1:

If t m n h + h + τ ≥ t m+1 n h + τ m+1 n , define a function τ n (t n ) as τ n (t n ) = t n -t m n h, t n ∈ Ω, (16)
where

τ m n ≤ τ n (t n ) ≤ (t m+1 n -t m n )hτ m+1 n ≤ hτ . Case 2: If t m n h + h + τ < t m+1 n h + τ m+1 n
, since t m n < τ , it can be easily checked that there exists a positive integer d M such that

t m n h + d M h + τ < t m+1 n h + τ m+1 n ≤ t m n h + d M h + h + τ for the time interval [t m n h + τ m n , t m n h + h + τ ) ∪ [t m n h + ∆ + h + τ m n , t m n h + ∆ + h + h + τ ) with ∆ + = 1, 2, . . . , d M , and d M = min l n |t m n h + τ m n + l n h ≥ t m+1 n h + τ m+1 n
. Therefore, the time interval Ω can be divided into the following subintervals

Ω = ∪ d M ∆=0 Ω ∆ , ∆ = 0, 1, . . . , d M , (17)
where

     Ω 0 = [t m n h + τ m n , t m n h + h + τ ) Ω ∆ = [t m n h + ∆ h + τ m n , t m n h + ∆ h + h + τ ) Ω d M = [t m n h + d M h + τ , t m+1 n h + τ m+1 n ) with ∆ = 1, 2, . . . , d M -1.
Define the following piecewise function

τ n (t n ) =      t n -t m n h, t n ∈ Ω 0 t n -t m n h -∆ h, t n ∈ Ω ∆ t n -t m n h -d M h, t n ∈ Ω d M . ( 18
)
Then it can be obtained that

     τ m n ≤ τ n (t n ) ≤ h + τ , t n ∈ Ω 0 τ m n ≤ τ ≤ τ n (t n ) ≤ h + τ , t n ∈ Ω ∆ τ m n ≤ τ ≤ τ n (t n ) ≤ h + τ , t n ∈ Ω d M .
Therefore, we have

τ τ m ≤ τ m n ≤ τ n (t n ) ≤ (h + τ ) τ M , t n ∈ Ω. ( 19
)
Based on the analysis above, for time interval Ω, in Case 1, define e n (t n ) = 0; in Case 2, define

e n (t n ) =      0, t n ∈ Ω 0 x n (t m n h) -x n (t m n h -∆ h), t n ∈ Ω ∆ x n (t m n h) -x n (t m n h -d M h), t n ∈ Ω d M .
Then according to ( 16) and ( 18), the following expression holds

e n (t n ) = x n (t m n h) -x n (t n -τ (t n )), t n ∈ Ω. (20)
Substituting ( 20) into [START_REF] Ji | Path planning and tracking for vehicle collision avoidance based on model predictive control with multiconstraints[END_REF], one has

xn (t n ) = e n (t n ) + x n (t n -τ n (t n )), t n ∈ Ω. (21)
It is assumed that system ( 9) is controlled over a CAN communication network with a state feedback controller. Due to the existence of communication network delays, it is unreasonable to assume that the controller shares the same premise variables with the system. Therefore, a fuzzy controller is designed as follows by using the IPM method [START_REF] Lam | Stability analysis and performance design for fuzzy-model-based control system under imperfect premise matching[END_REF], [START_REF] Peng | Observer-based Non-PDC control for networked T-S fuzzy systems with an event-triggered communication[END_REF]:

Controller Rule r: IF σ 1 (lh) is H 1, (σ 1 (lh)), σ 2 (lh) is H 2, (σ 2 (lh)), and σ 3 (lh) is H 3, (σ 3 (lh)), THEN u(t) = K r x(t), t ∈ [lh, (l + 1)h), (22)
where

r ∈ {1, 2, . . . , 8}, x(t) [x 1 (t m 1 h), x2 (t m 2 h), x3 (t m 3 h), x4 (t m 4 h)]
T is the system state vector reassembled from the latest available data received by the controller, and K r is the controller gain to be designed.

Remark 7. The vehicle's lateral velocity is often not directly measurable or costly to measure directly. In this case, state estimation methods such as the Kalman filter and its extended form can be applied; see [START_REF] Qin | A Lateral and Longitudinal Dynamics Control Framework of Autonomous Vehicles Based on Multi-Parameter Joint Estimation[END_REF]- [START_REF] Zhang | Takagi-Sugeno Fuzzy-based Kalman Filter Observer for Vehicle Side-slip Angle Estimation and Lateral Stability Control[END_REF] and the reference therein.

Let e(t) [e 1 (t 1 ), e 2 (t 2 ), e 3 (t 3 ), e 4 (t 4 )] T and x(t-τ (t)) [x 1 (t 1 -τ 1 (t 1 )), . . . , x 4 (t 4 -τ 4 (t 4 ))] T , where t n ∈ Ω. According to ( 21) and ( 22), the fuzzy controller can be expressed as follows by employing fuzzy reasoning

u(t) = 8 r=1 µ r (σ(lh))K r [e(t) + x(t -τ (t))] , (23)
where the membership factors µ r (σ(lh)), shortened as µ r µ r (σ(lh)), are defined in [START_REF] Milani | Smart autodriver algorithm for real-time autonomous vehicle trajectory control[END_REF] with η j , and σ(t) replaced by µ r and σ(lh), respectively. Combining ( 9) and ( 23), it yields the closed-loop fuzzy system as follows

ẋ(t) = 8 j=1 8 r=1 η j µ r [A jr x(t) + B j K r x(t -τ (t)) +B j K r e(t) + B 1j ω(t)] . (24)

E. Problem formulation

In the following design process, we aim to improve the following performance of the AGV while maintaining its lateral stability. Therefore, the controlled output vector is chosen as follows

z(t) = Cx(t), (25)
where C = diag(q 1 ,q 2 ,q 3 ,q 4 ), q n is the weighting coefficient reflecting the degree of importance, and C = I.

We can now formulate the main problem of this study as designing an appropriate event-triggered fuzzy controller in form (23) using the DETCM (11) so that 1) closed-loop system (24) with a time-varying parameter is asymptotically stable when the external disturbance ω(t) ≡ 0; 2) under zero initial conditions, the effect from external input ω(t) to signal z(t) satisfies

z(t) 2 < γ ω(t) 2 (26)
for all nonzero ω(t) ∈ L 2 [0, ∞) with an H ∞ performance γ > 0. The following lemmas will be used later for the proof of the main results. Lemma 1. [START_REF] Li | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication[END_REF] For given positive scalars 0 ≤ τ m ≤ τ M , 0 > 0 and γ > 0, closed-loop system (24) is asymptotically stable and satisfies desired condition (26) if there exist positive definite matrices P , Q 1 , Q 2 , R 1 , R 2 , Φ, and feedback gains K r such that (j, r = 1, 2, . . . , 8)

Ψ jr =   Ψ 11 jr Ψ 12 jr Ψ 13 jr * Ψ 22 Ψ 23 jr * * Ψ 33   < 0, (27)
where

Ψ 11 jr =   Σ 11 jr P B j K r R 1 * Σ 22 R 2 * * Σ 33   , Ψ 12 jr =   0 P B j K r P B 1j R 2 Φ 0 0 0 0   , Σ 11 jr = P A j + A T j P + Q 1 + Q 2 -R 1 , Σ 22 = -2R 2 + Φ, Σ 33 = -Q 1 -R 1 -R 2 , Ψ 13 jr =   τ m A T j ∆τ A T j C T τ m K T r B T j ∆τ K T r B T j 0 0 0 0   , Ψ 22 = diag -Q 2 -R 2 , (1 -0 ) Φ, -γ 2 I , Ψ 23 jr =   0 0 0 τ m K T r B T j ∆τ K T r B T j 0 τ m B T 1j ∆τ B T 1j 0   , Ψ 33 = diag -R -1 1 , -R -1 2 , -I , ∆τ = τ M -τ m . Lemma 2.
[48] For given matrices Θ = Θ T , Υ, and Γ of appropriate dimensions, and F (t) satisfying F T (t)F (t) ≤ I, the following inequality Θ + ΥF (t)Γ + (ΥF (t)Γ) T < 0 holds if and only if there exists a scalar ε > 0 such that

  Θ Υ εΓ T * -εI 0 * * -εI   < 0.
Lemma 3. [START_REF] Wang | Robust H∞ path following control for autonomous ground vehicles with delay and data dropout[END_REF] For matrices X, W > 0, and scalar κ > 0, the following conditions are equivalent (1)

(W -κ -1 X) T W -1 (W -κ -1 X) ≥ 0, (2) κ 2 W -2κX ≥ -XW -1 X.

III. MAIN RESULTS

The following section derives a sufficient condition that ensures the asymptotic stability of closed-loop system [START_REF] Yang | Path tracking control for underactuated vehicles with matched-mismatched uncertainties: An uncertainty decomposition based constraint-following approach[END_REF] with DETCM.

Theorem 1. For the given constants γ, h, 0 , τ m , τ M (0 < τ m ≤ τ M ), and the membership functions satisfying µ r -λ r η r > 0 (0 < λ r ≤ 1), closed-loop system ( 24) is asymptotically stable with control gains K r if there exit symmetric positive definite matrices P , Q 1 , Q 2 , R 1 , R 2 , Φ, and arbitrary positive definite matrices Λ j of appropriate dimensions such that the following matrix inequality conditions hold for any j, r = 1, 2, . . . , 8:

Ξ jr -Λ j < 0, (28)
λ j Ξ jj + (1 -λ j )Λ j < 0, (29)
λ r Ξ jr + λ j Ξ rj + (1 -λ r )Λ j + (1 -λ j )Λ r < 0, j < r, (30)
where

Ξ jr = Ξ 11 jr Ξ 12 jr * Ξ 22 , Ξ 11 jr = Ψ 0 jr , Ξ 22 = diag -ε 1 I, -ε 1 I , Ξ 12 jr = E T j P 0 0 0 0 0 τ m E T j ∆τ E T j 0 ε 1 G 1 ε 1 G 2 K r 0 0 ε 1 G 2 K r 0 0 0 0 T ,
and Ψ 0 jr can be obtained from ( 27) by replacing A j and B j with A 0j and B 0j , respectively. Proof . Based on Lemma 1, by recalling the uncertainties defined in [START_REF] Xu | Design, analysis, and experiments of preview path tracking control for autonomous vehicles[END_REF], we obtain that

Ψ jr = Ψ 0 jr + W F Π + (W F Π) T < 0, (31)
where W T [E T j P ,0,0,0,0,0,τ m E T j , ∆τ E T j ,0], Π [G 1 ,G 2 K,0,0,G 2 K,0,0,0,0], and Ψ 0 jr can be obtained from ( 27) by replacing A j and B j with A 0j and B 0j , respectively. By using Lemma 2, inequality ( 31) is equivalent to

Ξ jr =   Ψ 0 jr W ε 1 Π T * -ε 1 I 0 * * -ε 1 I   < 0. ( 32
)
Then, for vector ξ(t) with appropriate dimensions, we have

8 j=1 8 r=1 η j µ r ξ T (t)Ξ jr ξ(t) < 0. ( 33
)
Consider a slack matrix

8 j=1 8 r=1 η j (µ r -η r )Λ j = 8 j=1 η j ( 8 r=1 η r - 8 r=1 µ r )Λ j ≡ 0
as described in [START_REF] Lam | Stability analysis and performance design for fuzzy-model-based control system under imperfect premise matching[END_REF]. Substituting these terms into (33) yields

8 j=1 8 r=1 η j µ r ξ T (t)Ξ jr ξ(t) = 8 j=1 η 2 j ξ T (t)[λ j Ξ jj +(1 -λ j )Λ j ]ξ(t) + 8 j=1 j<r η j η r ξ T (t)[λ r Ξ jr + λ j Ξ rj +(1 -λ r )Λ j + (1 -λ j )Λ r ]ξ(t) + 8 j=1 8 r=1 η j (µ r -λ r η r )ξ T (t)[Ξ jr -Λ j ]ξ(t).
(34) Then if µ r -λ r η r > 0 and ( 28)-( 30) hold for all r = 1, 2, . . . , 8, desired condition (26) can be guaranteed. This completes the proof.

Remark 8. Although the introduction of membership function design condition µ r -λ r η r > 0 leads to conservative stability analysis results [START_REF] Lam | Stability analysis and performance design for fuzzy-model-based control system under imperfect premise matching[END_REF], more relaxed stability analysis and controller synthesis results can be developed [START_REF] Peng | Observer-based Non-PDC control for networked T-S fuzzy systems with an event-triggered communication[END_REF], especially for NCSs with communication network delays.

Remark 9. In this study, due to network-induced delay, the fuzzy controller does not share the same premise variables as the T-S fuzzy mode, i.e., µ r = η r , so the IPM method is used to derive Theorem 1. If µ r = η r in [START_REF] Yang | Path tracking control for underactuated vehicles with matched-mismatched uncertainties: An uncertainty decomposition based constraint-following approach[END_REF], we can use similar perfect premise matching methods, e.g., the parallel distribution compensation (PDC) technology [START_REF] Zhang | A novel robust event-triggered fault tolerant automatic steering control approach of autonomous land vehicles under in-vehicle network delay[END_REF], [START_REF] Li | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication[END_REF], to get the corresponding results. Therefore, the PDC technique can be regarded as a special case of the proposed method.

Although Theorem 1 can guarantee the stability and the performance of closed-loop system [START_REF] Yang | Path tracking control for underactuated vehicles with matched-mismatched uncertainties: An uncertainty decomposition based constraint-following approach[END_REF], the controller gain is coupled with unknown matrix variables, and matrix inequalities ( 28)-( 30) are non-convex. On this basis, controller gains in form ( 22) can be obtained in the following theorem.

Theorem 2. For the given constants γ, h, 0 , τ m , τ M (0 < τ m ≤ τ M ), and the membership functions satisfying µ r -λ r η r > 0 (0 < λ r ≤ 1), closed-loop system ( 24) is asymptotically stable with control gains K r if there exist symmetric positive definite matrices P , Φ,

Q 1 , Q 2 , R 1 , R 2 ,
and arbitrary positive definite matrices Λ j of appropriate dimensions such that the following linear matrix inequality conditions hold for any j, r = 1, 2, . . . , 8:

Ξ jr -Λ j < 0, (35)
λ j Ξ jj + (1 -λ j ) Λ j < 0, (36)
λ r Ξ jr + λ j Ξ rj + (1 -λ r ) Λj + (1 -λ j ) Λ r < 0, j < r, (37)
where

Ξ jr =      Ξ 11 jr Ξ 12 jr Ξ 13 jr Ξ 14 jr * Ξ 22 Ξ 23 jr Ξ 24 jr * * Ξ 33 Ξ 34 jr * * * Ξ 44 jr      , Ξ 11 jr =    Σ 11 jr B 0j K r R 1 * -2 R 2 R 2 * * Σ 33    , Σ 11 jr = A 0j P + P A T 0j + Q 1 + Q 2 -R 1 , Σ 33 = -Q 1 -R 1 -R 2 , Ξ 12 jr =   0 B 0j K r B 1j R 2 0 0 0 0 0   , Ξ 14 jr =   E ε 1 P G T 1 0 0 ε 1 K T r G T 2 P 0 0 0   , Ξ 13 jr =   τ m P A T 0j ∆τ P A T 0j P C T τ m K T r B T 0j ∆τ K T r B T 0j 0 0 0 0   , Ξ 22 = diag -Q 2 -R 2 , -0 κ 2 0 Φ -2κ 0 P , -γ 2 I , Ξ 23 jr =   0 0 0 τ m K T r B T 0j ∆τ K T r B T 0j 0 τ m B T 1j ∆τ B T 1j 0   , Ξ 24 jr =   0 0 0 0 ε 1 K T r G T 2 P 0 0 0   , Ξ 34 jr =   τ m E j 0 0 ∆τ E j 0 0 0 0 0   , Ξ 33 = diag κ 2 1 R 1 -2κ 1 P , κ 2 2 R 2 -2κ 2 P , -I , Ξ 44 = diag -ε 1 I, -ε 1 I, -Φ .
In addition, the fuzzy control gains and weight matrix can be determined by K r = K r P , and Φ = Φ -1 , respectively.

Proof . By pre-and post-multiplying [START_REF] Shi | Road-curvature-range-dependent path following controller design for autonomous ground vehicles subject to stochastic delays[END_REF] with diag(P -1 ,P -1 ,P -1 ,P -1 ,P -1 ,I,I,I,I,I,I) and letting

P = P -1 , Q 1 = P Q 1 P , Q 2 = P Q 2 P , R 1 = P R 1 P , R 2 = P R 2 P , K r = K r P , Φ = Φ -1 , we have     E 11 jr E 12 jr E 13 jr E 14 jr * E 22 E 23 jr E 24 jr * * E 33 E 34 jr * * * E 44 jr     < 0, (38)
where

E 11 jr =    Σ 11 jr B 0j K r R 1 * T 22 Σ 23 * * Σ 33    , E 12 jr =   0 B 0j K r B 1j R 2 P Φ -1 P 0 0 0 0   , E 13 jr = Ξ 13 jr , E 14 jr =   E j ε 1 P G T 1 0 ε 1 K T r G T 2 0 0   , E 24 jr =   0 0 0 ε 1 K T r G T 2 0 0   , E 22 = diag -Q 2 -R 2 , (1 -0 ) P Φ -1 P , -γ 2 I , E 23 jr = Ξ 23 jr , E 33 = diag -P R -1 1 P , -P R -1 2 P , -I , E 34 jr = τ m E T j ∆τ E T j 0 0 0 0 T ,E 44 = diag (-ε 1 I, -ε 1 I) , T 22 = -2 R 2 + P Φ -1 P .
Note that -P # -1 P are nonlinear terms, where # stands for R 1 and R 2 , respectively. From Lemma 3, those nonlinear terms can be replaced with κ 2 k # -2κ k P (k = 1, 2). It is then not difficult to derive Ξ jr in ( 35) from ( 38) by using the Schur complement and Lemma 3 to deal with the nonlinear term -P Φ -1 P . This completes the proof.

Remark 10. For CETCM, only the matrix Φ > 0 is required [START_REF] Zhang | A novel robust event-triggered fault tolerant automatic steering control approach of autonomous land vehicles under in-vehicle network delay[END_REF], [START_REF] Li | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication[END_REF]. In this case, let Φ P Φ -1 P , then weight matrix Φ with the CETCM is given by Φ = P -1 Φ P -1 , where Φ and P can be obtained by solving [START_REF] Tallapragada | Decentralized event-triggering for control of nonlinear systems[END_REF]. However, for DETCM, since the block diagonal structure of Φ cannot be guaranteed, the above variable substitution method is not applicable. From linear algebra, the inverse of a block diagonal matrix, if it exists, is also a block diagonal matrix. Given this, denote Φ Φ -1 and P P -1 , then one has P Φ P = P Φ -1 P . On this basis, using the Schur complement and Lemma 3, Φ can be solved directly according to Theorem 2, thereby ensuring the block diagonal structure of matrix Φ.

In general, it is desired that the H ∞ performance index γ is as small as possible. In this case, its minimum value can be obtained by the following corollary.

Corollary 1. The minimum H ∞ performance γ * in Theorem 2 can be found by solving the following convex optimization problem:

γ * = min γ s.t. [START_REF] Ge | Dynamic event-triggered scheduling and control for vehicle active suspension over controller area network[END_REF], [START_REF] Li | Adaptive-event-triggerbased fuzzy nonlinear lateral dynamic control for autonomous electric vehicles under insecure communication networks[END_REF], and (37).

It is necessary mention that the slack matrix introduced in Theorem 2 provides more design flexibility, thereby alleviating the conservatism of the results. If the slack matrix is not introduced, we have the following corollary.

Corollary 2. For the given constants γ, h, 0 , τ m , τ M (0 < τ m ≤ τ M ), and the membership functions satisfying µ r -λ r η r > 0 (0 < λ r ≤ 1), closed-loop system (24) is asymptotically stable with control gains K r if there exist symmetric positive definite matrices P , Φ, Q 1 , Q 2 , R 1 , and R 2 of appropriate dimensions such that the following linear matrix inequality conditions hold for any j, r = 1, 2, . . . , 8:

Ξ jr < 0, (39)
λ j Ξ jj < 0, (40)
λ r Ξ jr + λ j Ξ rj < 0, j < r. (41)
Similar to Corollary 1, we can achieve the following corollary. IV. NUMERICAL SIMULATION This section validates the effectiveness of the proposed method with numerical simulation.

A. Simulation settings

Two simulation cases, i.e., the double-lane change and lane change maneuvers, are constructed in the CarSim-Simulink joint-simulation environment. Furthermore, a CAN model is built through Simulink/SimEvents, which is composed of one bus model and three network node models, and those who are interested can refer to [START_REF]Effects of communication delays on an ABS control system -MATLAB & Simulink[END_REF] for details. An E-Class SUV in CarSim is selected as the controlled AGV, and its normal parameters are listed in Table II.

In this study, the sampling interval of sensors is 0.01s, and the minimum and maximum CAN-induced delay are τ m = 0.001s, and τ M = 0.02s, respectively. Because of this communication delay, the membership factors µ r and η r will depend on different premise variables, as discussed in Section II-C. Considering that the vehicle mass won't change in a short period, to simplify the problem, we set the vehicle mass to its nominal value m 0 when determining the value of λ r . In order to ensure membership function design condition µ r -λ r η r > 0 always holds, as we can see from [START_REF] Milani | Smart autodriver algorithm for real-time autonomous vehicle trajectory control[END_REF] and [START_REF] Li | Velocity-based robust fault tolerant automatic steering control of autonomous ground vehicles via adaptive event triggered network communication[END_REF], the main factor that affects λ r is the change in vehicle speed, i.e., longitudinal acceleration a x . For convenience, we call λ r the membership function parameter. To determine the value of the membership function parameter, we examine some typical vehicle test cycles, such as NEDC, UDDS, and WLTC, whose velocity and acceleration profiles are shown in Fig. 3. There is no doubt that the acceleration of the above vehicle test cycles is bounded, and the supre-and infimum accelerations are denoted by a xsup and a xinf , respectively. Therefore, the speed change due to communication delay is also bounded, and we have that

∆v x = F • τ M • a xsup , ∆v x = F • τ M • a xinf , ( 42
)
where F is the scale factor. Then we can use Algorithm 1 to determine λ r .

In the simulation, the uncertain cornering stiffness is assumed to be 10% of the normal value. For given scalars 0 = 100, κ 0 = 0.2, κ 1 = 0.15, κ 2 = 0.1, and λ r , the corresponding control gains K r and matrix Φ can be obtained by using Corollary 1 and the YALMIP toolbox [START_REF] Lofberg | Yalmip: A toolbox for modeling and optimization in MATLAB[END_REF]. Furthermore, the minimal γ obtained is 92.25, which is smaller than the minimal γ obtained by Corollary 3 of 94.34.

To highlight the performance of the proposed DETCMbased fuzzy feedback controller, a decentralized time-triggered communication mechanism (DTTCM) based controller is used for comparison, which can be derived from [START_REF] Chen | Path following control of autonomous four-wheel-independent-drive electric vehicles via secondorder sliding mode and nonlinear disturbance observer techniques[END_REF] by letting n (t) = 0. The following transmission rate (TR) is adopted as a performance metric of communication efficiency

TR = N 1 N 2 • 100%, (43)
where N 1 denotes the number of transmitted sample signals released by the relevant event generator, and N 2 represents the total number of sampled signals, respectively.

Algorithm 1 Determine the value of the membership function parameter λ r .

Input: ∆v x , ∆v x , v x , v x , m, m, m 0 Output: λ r 1: function H ( σ, σ, σ) 2: if σ > σ then σ = σ end if 3: if σ < σ then σ = σ end if 4: H 1 (σ) = (σ -σ)/(σ -σ), H 2 (σ) = 1 -H 1 (σ) 5:
return H 1 , H 2 6: end function

7: function M (H 1,1 , H 1,2 , H 2,1 , H 2,2 , H 3,1 , H 3,2 ) 8:
Calculate η 1 ∼ η 8 according to [START_REF] Milani | Smart autodriver algorithm for real-time autonomous vehicle trajectory control[END_REF] 9:

return η 1 ∼ η 8 10: end function 11:

12: λ r = ones(1, 8), H 3,1 , H 3,2 ← H ( 1 m0 , 1 m , 1 m ) 13: for v x = v x : dv x : v x do 14: H 1,1 , H 1,2 ← H (v x , v x , v x ) 15: H 2,1 , H 2,2 ← H ( 1 vx , 1 v x , 1 vx ) 16
: for v x = v x + ∆v x : δv x : v x + ∆v x do 18:

η 1 ∼ η 8 ← M (H 1,1 , H
H 1,1 , H 1,2 ← H (v x , v x , v x )
19:

H 2,1 , H 2,2 ← H ( 1 v x , 1 v x , 1 vx ) 20: η 1 ∼ η 8 ← M (H 1,1 , H 1,2 , H 2,1 , H 2,2 , H 3,1 , H 3,2 )
21:

for i = 1 : 1 : 2 3 do can also produce similar lateral velocity and yaw rate, as depicted in Fig. 6. To compare the path tracking performance with different triggering mechanisms, the statistical metrics in the simulation process, namely, the root mean square (RMS) and maximum (MAX) value of lateral offset and heading error, are shown in Table III. As we can see, these two triggering mechanisms are capable of achieving similar path tracking results and maintaining maximum lateral and heading deviations within small ranges, which are about 0.10m for lateral offset and 0.02rad for heading error.

To evaluate the communication performance of DETCM, the release instant of each sensor is highlighted with corresponding symbols in Fig. 5 and Fig. 6, from which it can be seen that the data transmission of sensors exhibits obvious sparse features. Further evaluation results, including the number of sampling data released by the event generator, TR and performance improvement, are illustrated in Table IV. It can be seen that the number of release data per sensor with DETCM is 124, 121, and 111 times, respectively, while DTTCM is 1400 times for each sensor. This indicates that DETCM greatly saves bandwidth resources by transmitting much less sampled data.

By projecting the sensor release values, i.e., the value received by the controller, onto the bottom horizontal plane, it can be seen that the previous release value will remain unchanged until a new one is received. By using these received release values, the control input, i.e., front wheel steering angle, can be obtained, which shows obvious step changes with slight jitter due to the event-triggered mechanism. The front wheel steering angle and the corresponding global trajectories of the AGV are shown in Fig. 7.

C. Scenario B: lane change maneuver

In the simulation, the AGV is supposed to complete a lane change maneuver at varying longitudinal velocities. Fig. 8 exhibits the reference trajectory, path curvature, and longitudinal velocity profile of the AGV in Scenario B. Fig. 9 shows the results for lateral offset and heading error, indicating that DETCM can achieve a comparable path tracking performance with a much lower release frequency than DTTCM. As shown in Table III, both mechanisms guarantee that path tracking deviations are within the safe region [START_REF] Zhang | A novel robust event-triggered fault tolerant automatic steering control approach of autonomous land vehicles under in-vehicle network delay[END_REF] and have similar statistical properties when comparing the RMS and maximum values of lateral and heading deviations for event-triggering and time-triggering cases. Furthermore, as illustrated in Fig. 10, the vehicle's lateral dynamics, such as its lateral velocity and yaw rate, also exhibit similar characteristics.

In addition, DETCM has obvious advantages in release frequency, as shown in Table IV, while guaranteeing satisfactory path tracking performance. The results shows that, on average, TR is only 13.4% with DETCM compared to DTTCM. The above results further verify the effectiveness of the proposed DETCM in saving communication resources. Finally, the Furthermore, a co-design method is proposed for decentralized event-triggered communication scheduling and IPMbased path tracking control. Simulations have demonstrated that the proposed scheme can guarantee reliable path tracking performance and reduce communication occupancy by an average of 91.5% and 88.6% in two typical scenarios, respectively, compared with the DTTCM strategy.

Our future goal is to design a path tracking controller that uses observer-or output-based feedback. In addition, the impact of measurement noise on path tracking performance during practical implementation is also worthy of further study.

Fig. 1 .

 1 Fig. 1. A decentralized event-triggered communication scheme for AGVs with distributed sensors via an in-vehicle network.

Fig. 2 .

 2 Fig. 2. An example of a CAN signal transmission sequence diagram.

Corollary 3 .

 3 The minimum H ∞ performance γ * in Corollary 2 can be obtained by solving the following convex optimization problem:γ * = min γ s.t. (39),[START_REF] Lam | Stability analysis and performance design for fuzzy-model-based control system under imperfect premise matching[END_REF], and (41).

22 : 2 )Fig. 3 .

 2223 Fig. 3. Velocity and acceleration profiles for NEDC, UDDS, and WLTC vehicle test cycles.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Reference trajectory, road curvature, and longitudinal vehicle velocity in Scenario A, where the road curvature is within [-4.8, 4.8] • 10 -3 m -1 , and the longitudinal vehicle velocity ranges within [40, 50]km/h.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Results in Scenario A. The blue and red solid curves represent the lateral vehicle dynamic of the AGV with DTTCM and DETCM, respectively. The orange stairstep curves show the release values of lateral velocity and yaw rate that satisfy the relevant triggering conditions, and the release moments are marked with green solid triangles and squares, respectively.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Reference trajectory, road curvature, and longitudinal vehicle velocity in Scenario B, where the road curvature is within [-0.005, 0.005]m -1 , and the longitudinal vehicle velocity varies within [40, 60]km/h.

Fig. 10 .

 10 Fig. 10. Results in Scenario B. The blue and red solid curves represent the lateral vehicle dynamic of the AGV with DTTCM and DETCM, respectively. The orange stairstep curves show the release values of lateral velocity and yaw rate that satisfy the relevant triggering conditions, and the release moments are marked with green solid triangles and squares, respectively.

Fig. 11 .

 11 Fig. 11. The front wheel steering angle and global trajectories of the AGV in Scenario B.

  1,2 , H 2,1 , H 2,2 , H 3,1 , H 3,2 )

17:

This work was supported by the National Natural Science Foundation of China (Grants 52222216, 52172384 and 52002126), S&T Innovation Program of Hunan Province (Grant 2021RC3048), Hunan Provincial Natural Science Foundation of China (Grants 2021JJ40086 and 2021JJ40095), and the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body with 61775006.