Thao Dang
email: thao.dang@univ-grenoble-alpes.fr

Alexandre Donzé

Inzemamul Haque

Nikolaos Kekatos
email: nkekatos@csd.auth.gr

Indranil Saha
email: isaha@cse.iitk.ac.in

Counter-Example Guided Imitation Learning of Feedback Controllers from Temporal Logic Specifications

We present a novel method for imitation learning for control requirements expressed using Signal Temporal Logic (STL). More concretely we focus on the problem of training a neural network to imitate a complex controller. The learning process is guided by efficient data aggregation based on counterexamples and a coverage measure. Moreover, we introduce a method to evaluate the performance of the learned controller via parameterization and parameter estimation of the STL requirements. We demonstrate our approach with a flying robot case study.

I. INTRODUCTION

The aim of this work is to integrate formal specification and validation techniques in the Imitation Learning (IL) methodology for synthesizing feedback controllers for complex dynamical systems. While formal methods have the advantage of rigorous formalization and reasoning, they are very limited in the complexity and scalability of the problems that can be practically solved. Imitation Learning, also known as learning from demonstrations, involves the process of learning how to mimic the behavior of an expert by observing their actions in a given task [START_REF] Saha | Learning from demonstration[END_REF]. It has many successful applications in various fields such as robotics, natural language processing, image and speech recognition.

In this work, we focus on the problem of training a neural network (NN) (playing the role of a learner) to imitate a complex controller (playing the role of an expert). The ultimate goal is to replace this complex controller with a trained NN. NNs have long been used to control dynamical systems from inverted pendulums to quadcopters, learning from scratch to control the plant by maximizing an expected reward, e.g. [START_REF] Hagan | An introduction to the use of neural networks in control systems[END_REF], [START_REF] Nicol | Robust neural network control of a quadrotor helicopter[END_REF]. NNs can also be trained to replace an existing controller that is unsatisfactory for non-functional reasons, e.g., computationally expensive (consider modelpredictive control [START_REF] Garcia | Model predictive control: Theory and practice-a survey[END_REF]), slow, or energy intensive. A welltrained NN controller can provide similar control performance much faster and is readily implemented on cheap and energy-efficient embedded platforms [START_REF] Varshney | Deepcontrol: Energy-efficient control of a quadrotor using a deep neural network[END_REF].

To make such an imitation learning framework more formal and more efficient, we add the following novel features:

(i) a formalization of performance evaluation for both the learner's and expert's policies using their abilities to satisfy requirements specified by temporal logic, (ii) a leverage of the power of existing temporal logic property falsification tools to create training data that matter, (iii) a new method of data aggregation in order to guarantee a good performance of NN in terms of imitation and generalization.

To explain these features, let us first point out some major difficulties in this problem. Training a NN to imitate a feedback controller is more complex than the problem of approximating a function using pairs of input and output values, since feedback controllers can themselves be stateful dynamical systems. We identify the following difficulties in data generation by executing the nominal controller in closed loop:

• Infinite behavior space. The behavior space is not only large but can also be infinite. It is thus important to define a coverage measure to quantify how representative the generated training data is. • Non-uniform accuracy. Depending on the control requirement, the NN may need to be very precise around some region of the state space while in other regions a rough approximation is acceptable. The problem of non-uniform accuracy is particularly pronounced when the requirement depends on time or sequences of events. This is frequently the case in control applications, where properties such as rise time, settling time, and overshoot are typical. We consider complex properties that can include not only time but also causal relationships. They can be described in Signal Temporal Logic (STL), a formal language that finds widespread use in formal methods and increasing adoption in industry [START_REF] Bartocci | Specification-based monitoring of cyber-physical systems: a survey on theory, tools and applications[END_REF].

While observing closed-loop behaviors may reduce the number of behaviors to be sampled, we still need to find good training samples that are relevant to an STL property. To do this, we find counter-examples that are closed-loop behaviors violating this property by leveraging the existing falsification tools [START_REF] Donzé | Breach, A toolbox for verification and parameter synthesis of hybrid systems[END_REF]. A falsification process can also be useful in providing correctness guarantees for the resulting NN. Indeed, if no counter-example is found after a sufficiently large number of scenarios, we consider the NN controller satisfactory and stop. If a counter-example is found, we replay the nominal controller from the counter-example situation in order to obtain new training data, and retrain the neural network. This new data creation is crucial for the efficiency of the process of correcting counter-examples as well as assuring good generalization of the NN.

Related Work. Several comprehensive surveys exist [START_REF] Osa | An algorithmic perspective on imitation learning[END_REF] on imitation learning. A common approach is behavioral cloning [START_REF] Michie | Cognitive models from subcognitive skills[END_REF] for which the main problem is compounding error, when the assumption of independent and identically distributed data between training and testing data is not valid for sequential predictions. A common solution to this problem is Dataset Aggregation (DAgger) which was proposed in [START_REF] Ross | A reduction of imitation learning and structured prediction to no-regret online learning[END_REF]. It is an iterative algorithm which improves on behavioral cloning by training on a dataset that better resembles the observations the trained policy is likely to encounter. In this paper, we propose a similar approach in the sense that the expert is queried for good actions and new data are created and aggregated in the dataset. However, our goal is to design an approach that learns the dynamics of desirable behavior and not the dynamics of possible behavior. Applications of imitation learning for Model Predictive Control have been proposed in [START_REF] Acerbo | Safe imitation learning on real-life highway data for human-like autonomous driving[END_REF]. A recent approach to "compress" an MPC into a NN using robust tube MPC is proposed in [START_REF] Tagliabue | Efficient guided policy search via imitation of robust tube MPC[END_REF]. In [START_REF] Chow | Parallelized control-aware motion planning with learned controller proxies[END_REF], the need to replace an MPC controller with a NN is exemplified for planning purposes. Our approach is different from the previous works as we use counterexample guided synthesis and a combination of coverage and PSTL formal specifications. There are counter-examplebased approaches similar to ours though -for instance, some use counter-example exploration (adversarial sample) to train NNs that seek to satisfy a given property expressed in temporal logic (see [START_REF] Yaghoubi | Worst-case Satisfaction of STL Specifications using Feedforward Neural Network Controllers: A Lagrange Multipliers Approach[END_REF]) or through a reference trajectory (see [START_REF] Clavière | Trajectory tracking control for robotic vehicles using counterexample guided training of neural networks[END_REF]). The closest to our work is [START_REF] Clavière | Trajectory tracking control for robotic vehicles using counterexample guided training of neural networks[END_REF], where the behavior of an MPC is approximated with a NN to enable a robot to follow a reference trajectory. The NN is refined by generating additional training data from counter-examples. However, unlike our framework, their approach is limited to memoryless controllers, and they use tracking closeness as the sole criterion to identify counter-examples. In our experience, a NN need not always closely track the nominal behavior to satisfy the specifications. It may have some characteristics that are better than the nominal controller, such as a smaller overshoot, or quicker stabilization in some areas of the state space. Such behaviors would be eliminated using their approach. The rest of the paper is organized as follows. In Section II, we formalize the imitation learning problem. This requires definitions of control requirements specified using Parametric Signal Temporal Logic. We also propose a notion of policy performance to quantify the difference between the policy of the learner and the expert which is necessary to assess the imitation quality. Subsequently, in Section III and Section IV, we describe our dataset aggregation-based learning methodology. Finally, we demonstrate our approach on a robotic case study in Section V.

II. CONTROLLER IMITATION LEARNING PROBLEM

We consider a continuous-time plant S with state x ∈ R n that is controlled by an input signal u, observed through an output signal y with dynamics1 : ẋ(t) = f (x(t), u(t)) and y(t) = ζ (x(t)). The control input u is computed by a discretetime controller C with state z ∈ R n z and z k+1 = f c (z k , y k ), u k = υ(z k , y k ), where y k is a discrete-time signal resulting from sampling the output y(•) with time step h. The continuous-time control u(•) is a piece-wise constant function defined as ∀t ∈ [kh, (k + 1)h] u(t) = u k with k = 0, 1, . . .. We denote the closed-loop system by C ||S.

A. Control Requirements

We are given a nominal controller satisfying some requirement that captures essential qualitative properties while allowing some quantitative behavioral flexibility. This requirement is expressed using Parametric Signal Temporal Logic (PSTL), a formalism suitable for various control performance properties [START_REF] Bartocci | Specification-based monitoring of cyber-physical systems: a survey on theory, tools and applications[END_REF]. We want to train a neural networkbased controller achieving performance comparable to that of the nominal controller, as measured by valid parameters of the PSTL requirement.

1) Signal Temporal Logic [START_REF] Bartocci | Specification-based monitoring of cyber-physical systems: a survey on theory, tools and applications[END_REF]: An STL formula ϕ consists of atomic predicates along with logical and temporal operators. Atomic predicates are defined over signal values and have the form g(y(t)) ∼ 0, where g is a scalar-valued function over the signal y evaluated at time t and ∼∈ {<, ≤ , >, ≥, =, ̸ =}. Temporal operators "always" (□), "eventually" (♢), and "until" (U ) have the usual meaning and are scoped using intervals of the form

(a, b), (a, b], [a, b), [a, b], or (a, ∞), where a, b ∈ R + 0 and a < b.
If I is a time interval, the following grammar defines the STL language.

ϕ := ⊤ | g(y(t)) ∼ 0 | ¬ϕ | ϕ 1 ∧ ϕ 2 | ϕ 1 U I ϕ 2 (1)
The ♢ operator is formally defined as ♢ I ϕ ≜ ⊤U I ϕ, and the □ operator is defined as □ I ϕ ≜ ¬(♢ I ¬ϕ). When omitted, the interval I is taken to be [0, ∞). The "always" operator in □ϕ conveys that from the current time point onwards, ϕ always holds. The "eventually" operator in ♢ϕ means that there exists a time point in the future where ϕ holds.

The "until" operator in ϕ 1 U ϕ 2 means that, starting from the current time point ϕ 1 should hold continuously until a future time point where ϕ 2 holds. Additionally, an interval I can be combined with the operators to bound their scope to a segment of time in the future rather than the whole. For example,

ϕ 1 U [a,b] ϕ 2 holds true at time t if ϕ 2 holds true at some point t ′ ∈ [t + a,t + b] and ϕ 1 is always true in [t,t ′ ].
2) Parametric Signal Temporal Logic [START_REF] Asarin | Parametric Identification of Temporal Properties[END_REF]: Parametric STL (PSTL) is a variant of STL which makes it possible to replace numeric constants in an STL formula with symbolic variables or parameters. For instance, the formula ϕ = □ [0,τ] (∥y(t)∥ < s) with two parameters τ and s expresses the requirement that during τ seconds, the norm of signal y should be less than s. Formally, a PSTL formula is concretized into a STL formula by composing it with a valuation, defined as a mapping from symbolic parameters to reals. As an example, consider valuation p : {τ → 2, s → 10}, then ϕ(p) is the STL formula ϕ(p) = □ [0,2] (∥y(t)∥ < 10).

Given a PSTL formula ϕ and a valuation p, a behavior γ satisfies ϕ(p) is denoted by γ |= ϕ(p). By extension, we say that a valuation p is satisfied by a controller C if for all behaviors γ of the closed-loop system C ||S, γ |= ϕ(p).

The problem of finding a valuation p such that C satisfies ϕ(p) is sometimes called mining and can be seen (and solved) as a learning problem. In [START_REF] Jin | Mining Requirements From Closed-Loop Control Models[END_REF], an approach is presented that works for a monotonic PSTL formula. Intuitively a formula is monotonic if its satisfaction is monotonic w.r.t. the valuation of each individual parameter. For example, ϕ = □ [0,τ] (∥y(t)∥ < s) is monotonic because if ∥y(t)∥ is always smaller than s between time 0 and τ, then clearly ∥y(t)∥ is smaller than s ′ for any s ′ > s and it is also smaller than s between time 0 and τ ′ for τ ′ ≤ τ. Formally, the set P of all valuations is a subset of R n p , where n p is the number of parameters in the formula. Let ⪯ be the standard partial order on R n p , i.e., p = (p 1 , . . . ,

p n p ) ⪯ p ′ = (p ′ 1 , . . . , p ′ n p ) iff ∀i p i ≤ p ′ i , then if ∀γ the Boolean function p → γ |= ϕ(p)
is monotonic in p, then the PSTL formula ϕ is monotonic. For illustration purposes, to characterize our controller performance, the PSTL formula Φ that we will use is as follows:

µ ov := ∥y(t)∥ > s ov , µ st := ∥y(t)∥ < s st ( 2
)
ϕ st := ¬µ st ⇒ ♢ [0,τ tr ] □ [0,τ st ] µ st (3)
Φ := □¬µ ov ∧ □ϕ st (4)
Equation ( 2) defines the atomic predicates which check at a given time whether the signal norm is above s ov (overshoot), or below s st (defining a stabilization region around the equilibrium). Equation (3) defines a formula requiring that if the system is not stabilizing (µ st not satisfied), then it should eventually stabilize, i.e., after at most τ tr seconds, µ st should remain true for at least τ st seconds.

We can then see that Φ is monotonic. This follows from the monotonicity of atomic predicates and temporal operators □ and ♢ and the fact that each parameter appears only once in each sub-formula [START_REF] Asarin | Parametric Identification of Temporal Properties[END_REF]. Monotonicity here is advantageous not only for the mining problem but also for computing a performance measure defined by Pareto fronts as discussed in the next section.

B. Control Policy Performance Measure

In imitation learning, it is essential to have an appropriate measure of performance of control policies, especially when it is unclear what reward function is being optimized [START_REF] Osa | An algorithmic perspective on imitation learning[END_REF]. In our framework, we use the relation between the parameters in the PSTL requirements to compare the performance of different controllers. E.g., for the stabilization requirement (4), for a given size s st of the neighborhood around the equilibrium, the smaller the stabilization time τ st is, the faster the controller is. Assume that P(Φ) (set of parameter valuations for Φ) is compact. Any controller C defines a partition of this set into falsified and valid formulas:

P(Φ) = False(C ||S, Φ) ∪ Valid(C ||S, Φ)
The False and Valid sets are separated by the set of Paretoefficient parameter values, also called the Pareto front [START_REF] Pareto | Manuel d'é conomie politique[END_REF]; that means no parameter can be improved without compromising the others. We argue that the relative volumes of the False (and Valid) sets can be used to measure and compare performance of controllers. More specifically, we define the following measure of similarity:

Definition 1 (Control Policy Similarity): Given a plant S and two controllers C and C ′ designed to satisfy a PSTL requirement Φ, the performance similarity between C and C ′ is defined as

σ S,Φ (C , C ′ ) = vol(False(C ′ ||S,Φ) vol(False(C ||S,Φ)
where vol is the volume of a set, assumed to be non-zero for False(C ||S, Φ). Exact volume computation is difficult in general but monotonicity makes it easy to compute under-approximations. Indeed, consider a finite set of parameters p 1 , . . . , p k in False(C ||S, Φ) and for each p i , define p ⊥ i the set of parameters dominated by p i according to ⪯. Intuitively, p ⊥ i is a hyper-box with largest corner p i . Then i p ⊥ i ⊂ False(C ||S, Φ) and

∑ i vol(p ⊥ i ) ≤ vol(False(C ||S, Φ)). Since p ⊥
i is an hyperbox, its volume computation is trivial. This approximation is illustrated in Figure 1.

C. Imitation Learning Problem Formulation

Problem 1 (Feedback Controller Imitation Learning): Given a plant S, a nominal controller C such that the closed-loop system C ||S satisfies a PSTL specification Φ, our problem is to learn a neural network controller N to imitate C such that

• the closed-loop system N ||S satisfies Φ, and • the performance similarity σ S,Φ (C , N ) is as small as possible. The learning guidance here is provided using positive examples, i.e. good behaviors, generated by the nominal controller which already satisfies the desired requirement. As we will see later, using parametric requirements allows more freedom in choosing nominal controllers satisfying some (minimal) performance, however to estimate the controller similarity in the learning process we estimate the actual Pareto-efficient parameters satisfied by a concrete nominal controller. Such a nominal controller may be complex and costly to execute and the ultimate goal is thus to use the learned NN controller to replace it. In the learning context, the nominal controller plays the role of a teacher that generates a desired control signal for a given system state which the NN should imitate.

In this paper, we mostly focus on the problem of how to iteratively train NN using examples (good behaviors) and counter-examples (bad behaviors).

III. FEEDBACK CONTROLLER LEARNING METHODOLOGY

We will explain our approach for solving Problem 1 via an example that uses the PSTL formula Φ defined in (4). The major steps of our approach are as follows. Since initially we do not know the concrete performance of the nominal controller, we can assume that we conservatively choose a parameter valuation p so that Φ(p) is satisfied by the nominal controller. We train a NN controller satisfying Φ(p) using an iterative neural network training approach which is detailed in the subsequent subsections.

We generate and accumulate the traces generated by both controllers during the process. We use these traces to approximate their False domain. Then, we compute their volumes to estimate their policy similarity. Retraining is needed if this similarity is not as small as desired. To create data for such retraining, a finer grid can be used.

A. Neural Network Structure and Training

Intuitively, the NN controller is trained based on the good closed-loop behaviors we want it to learn. Let γ = (x(•), u(•), y(•)) be a good closed-loop behavior, from which we extract the data of the form d γ = (x k , y k , u k ) k < K where x k , y k , and u k are respectively the state, output, and control values at time t k ; K is the discrete-time horizon (that is, the number of sampled time points). When many behaviors are considered, the data set D is the union of all d γ . We generate a neural network N to fit the data set D. The structure of the NN should capture the inputoutput relationships of the nominal controller C . We keep some past values to represent the memory needed to compute the output at each discrete step. The input of the NN is (y k-1 , . . . , y k-m y , u k-1 , . . . , u k-m u ) where n z = m y + m u represents the dimension of the state variable of the controller. The NN output is u k . To train the NN, we use a loss function defined via the Root Mean Square Error (RMSE):

1

n d n d ∑ k=1 (∥u k -u k ∥)

B. Coverage based Data Generation

In order to achieve a robust NN controller, we need to provide data representing diverse settings that the NN should learn to cope with. Note that the set of reachable states of Algorithm 1 Dataset aggregation-based training algorithm.

1: N 0 ← / 0, D 0 ← / 0, k ← 1 2: repeat 3: (D k , Status) ← getNewData (N k-1 , D k-1 ) 4: if D k ̸ = D k-1 then ▷ In this case D k-1 ⊂ D k 5: N k ← Train (D k ) 6: k ← k + 1 7: until D k = D k-1 or k > k max 8: return N k , Status
the system is infinite, we thus use a coverage measure based on ε-net [START_REF] Kolmogorov | ε-entropy and ε-capacity of sets in function spaces[END_REF] to quantify how well a finite set of sampled states covers the reachable set.

We propose a simple grid-based method to construct εnets satisfying a separation requirement. These notions of ε-net and ε-separated sets are important to measure function approximation quality, expressed roughly as how to obtain an accurate function approximation with a small number of function evaluations.

Let us assume that the state space is a box B r = [r, r] n . We use a grid G to partition B r into a set G of rectangular cells with equal side length 2ε, assuming for simplicity that (rr)/(2ε) is an integer. The set C of center points of all the cells in G is an ε-net of the state space. It can be proved that it is an ε-net with minimal cardinality and additionally a ε-separated set with maximal cardinality 2 .

Datasets constructed using ε-nets guarantee ε coverage. However, as we shall see later, the falsification procedure (to check if a neural network satisfies the requirement) uses optimization-based search algorithms which can explore many states outside the ε-nets. To estimate a coverage measure that better reflects the portion of the tested behaviors, we can use a finer grid G c and take the ratio between the number of cells visited by both the sampling and falsification procedures and the total number of cells in this grid G c .

IV. DATASET AGGREGATION-BASED TRAINING

The top-level iterative training algorithm implements a data aggregation method, inspired by [START_REF] Ross | A reduction of imitation learning and structured prediction to no-regret online learning[END_REF], which uses the current NN to generate new data (from examples and counter-examples) that will be aggregated to the whole dataset to train a new NN. This dataset aggregation method considers the coverage and separation measures discussed in the previous section, to enable the NN to generalize well and provide high confidence in the correctness of the final NN.

The dataset aggregation algorithm (Algorithm 1) determines whether it should generate new data for retraining or stop. It stops after a maximum number of iterations k max or as soon as the procedure responsible for providing new training samples fails to do so.

The training procedure is successful if it terminates with D k = D k-1 , i.e., no new data is found, and the Status returned by GetNewData is "No counter-example found". This GetNewData procedure is described in Algorithm 2.

Algorithm 2 New data acquisition procedure. CexTraces ← falsify (N ) 9:

if CexTraces ̸ = / 0 then 10:

(D new , Status) ← fixAndMerge (D, CexTraces)

else ▷ Success.

12:

D new ← D 13:
Status ← "No counter-example found."

Algorithm 3 Augmenting the training data from bad traces.

1: procedure FIXANDMERGE(D , CexTraces)

2:
NeighSamples ← gridFilter (CexTraces)\Cover(D)

3:

if NeighSamples = / 0 then 4:

Status ← "Counter-examples do not add new data."

5:

D new ← D 6:
else ▷ Get fixed traces from some bad samples 7:

NeighSamples ← selectNeigh (NeighSamples) 8:

FixedTraces ← simNominal (NeighSamples) 9:

D new ← gridFilter (D ∪ FixedTraces)

10:

Status ←"New data available for training."

In the first call of Algorithm 2, when no neural network has been trained yet and the data set is empty, it samples states using an ε-net over the initial set via the getInitSamples function and computes nominal traces from these initial states, that is traces generated by the nominal controller via the simNominal function. The gridFilter function collects samples from these traces and ensures that only one sample per grid cell is kept so that the data remains ε-separated. Indeed the gridFilter function "filters" the sampled states by removing the newly sampled states from the cells that are covered by existing data already. A subset of the remaining samples is then used to compute new nominal traces, producing new data. This step is illustrated in Fig. 2. At the subsequent calls, new data is obtained by testing the current neural network N k , looking for traces that violate the requirement using falsification (falsify function). The procedure fixAndMerge described in Algorithm 3 is called to produce new nominal traces and add data from these new nominal traces, in order to "fix" these counter-examples. Again, to keep samples well separated, new nominal traces are generated only from the samples resulting after applying gridFilter on the bad traces (CexTraces -Line 2). We also remove samples that are already covered by D (Cover(D)), represented as blue cells in Fig. 2).

Furthermore, in selectNeigh the samples close to the cells which are already covered have higher priority to be selected, which helps the neural net to generalize more easily. This can be seen in Fig. 2 where the green cells (containing new data selected for retraining) are close to the blue cells (containing current training data).

Algorithm 1 stops either when no new data is returned by Algorithm 2 or when k max is reached. In the first case (no new data), there are two situations:

• "No counter-example found": Successful case. The falsification procedure has failed to falsify the neural network controller, providing our strongest evidence that we have obtained a correct controller with test coverage at least ε. • "Counter-examples do not add new data.". This means that the grid is likely too coarse and the counterexamples do not allow visiting new cells. If the maximum number of iterations is reached, the two statuses above are still possible (both stopping conditions are met), otherwise, the status returned is: "New data available for training." which indicates that the user can resume the process using the data aggregated so far.

V. FLYING ROBOT CASE STUDY

This example is taken from Mathworks [START_REF] Mathworks | Imitate nonlinear MPC controller for flying robot[END_REF] and describes a model of a flying robot that is driven by a nonlinear model predictive controller. The flying robot has two thrusters to move it in a 2-D space. The state of the flying robot, denoted by x, consists of six components: x 1 , x 2 (horizontal and vertical coordinate) θ (robot thrust direction), and their derivatives ẋ1 , ẋ2 and θ . The thrusts are represented by u = (u 1 , u 2 ). The dynamics of the robot are given by ẍ1

= (u 1 + u 2 )•cos(θ ), ẍ2 = (u 1 +u 2 )•sin(θ ) and θ = α •u 1 +β •u 2 .
The parameters are α = 0.2 and β = 0.2. For each thrust, there is an operating range [-u max , u max ] with u max = 3. Considering the following set X 0 of initial conditions

X 0 = { x 1 (0), x 2 (0), θ (0), ẋ1 (0), ẋ2 (0), θ (0) s.t. x 1 (0), x 2 (0) ∈ [3.8, 3.8], θ (0) ∈ [-2.5, 2.5], ẋ1 (0), ẋ2 (0) ∈ [-1.6, 1.6], θ (0) ∈ [-0.8, 0.8] ,
the goal of the control input is to drive the flying robot from any state in X 0 to a region close to the origin and maintain it in this region indefinitely. We define y as y(t) = ∥x(t)∥, so that the problem becomes to stabilize y close to 0. The nominal controller is provided by a model predictive control (MPC) scheme which computes inputs at each step that minimizes y(t) over a given horizon. The simulation time is 15 seconds. To evaluate the performance of a controller for this problem, we used the PSTL formula Φ defined in Equation 4, where we set τ st to +∞ and considered overshoot s ov , transient time τ tr and stabilization region s st as variables to measure. We applied our algorithm with the STL formula Φ(p) with p = {s ov → 15, τ tr → 14, s st → 2}.

The inputs of NNs we trained correspond to the state variables of the system and the previous control input variables. They have RELU as activation functions, 6 hidden layers (each with 256 neurons), one scaling layer and one output layer. Figure 3 shows the performance evaluations of the nominal controller and a sample of different trained NN controllers obtained after 6 iterations, computed in around 120 minutes of computation time on a standard PC with an Intel Core i7 10700 processor and 64 Go of memory. After only two iterations, the NN controller manages to improve on the overshoot. However, looking at the False domain for (τ st , τ tr ), we can see that the stabilization region is larger than that of the MPC controller, meaning that neural networks have trouble stabilizing the robot close to the origin due to the inherent instability of the system at this state.

VI. CONCLUSION

In this paper, we have presented a framework for efficiently training a neural network-based controller by imitation learning using a dataset aggregation approach with several novel aspects. Most notably, the collection of data from the nominal (expert) controller is done at states where the trained controller caused the plant to fail according to a specification expressed in Signal Temporal Logic. Moreover, the same specification is parameterized and can be used to evaluate the performance of the trained controller and how far or how differently it behaves with respect to the nominal controller. The method was evaluated on a nonlinear robotic system with promising results. Further experiments will be conducted and different practical and theoretical questions remain to be explored but we believe that this work represents an interesting step in the direction of safer and more efficient imitation learning methods of complex control systems.

Fig. 1 .

 1 Fig. 1. Volume estimation of False parameter set. Each p i outside the Valid set is close to the Pareto front and defines a closed hyper-box p ⊥ i strictly included in False(Φ). Computing the volume of ∪ i p ⊥ i yields an under-approximation of vol(False(Φ).

1 :

 1 procedure GETNEWDATA(D , N )

Fig. 2 .

 2 Fig. 2. One iteration of the learning algorithm.

Fig. 3 .

 3 Fig. 3. Result of training NN controllers for the flying robot. Good performance is obtained after only 5 iterations. The red region (Nominal Controller False Domain) represents the valuations p for which Φ(p) are not satisfied by the nominal controller. The boundary of this region represents the Pareto front of the nominal controller. Other plots represent the Pareto fronts for several instances of the NN controllers computed for different iterations. Similarity with the nominal MPC controller is indicated in the legend.

  2 where u is the output of the nominal controller and u is the output of the NN. It is possible to use other loss functions such as MSE (Mean Square Error); in our experiments so far the MRSE metric is more convenient in terms of interpreting the effects of control input error. A data point is a pair of input and output values, the total number n d of data points is the number of data points per system behavior multiplied by the number of behaviors. The NN accuracy is defined by the training and validation errors, which are obtained from evaluating the loss function on the training and validation data.

External disturbance can be included in the system dynamics, and the data generation process for learning can then be straightforwardly extended to cover the disturbance space.

This cardinality determines the ε-entropy and ε-capacity of the state space[START_REF] Kolmogorov | ε-entropy and ε-capacity of sets in function spaces[END_REF].

* This work is partially supported by the Indo-French Collaborative research project FOVERAS funded by IFCPAR/CEFIPRA, joint French-Japanese ANR-JST project CyPhAI, and the Auvergne-Rhône-Alpes Region Project DetAI.


Girolamo Giordano

Massimo Migliori
email: massimo.migliori@unical.it

Giorgia Ferrarelli

Gianfranco Giorgianni

Francesco Dalena

Peng Peng

Maxime Debost

Philippe Boullay

Zhen Liu

Hailing Guo

Zi-Feng Yan

Svetlana Mintova

Passivated surface of high aluminum containing ZSM-5 by silicalite-1: synthesis and application in dehydration reaction

Keywords: Surface Passivation, Zeolites, Methanol dehydration, Acidity control

come

INTRODUCTION

In the past few decades, with the uncontrolled emission of greenhouse gases represented by CO2, the world has been increasingly threatened by the issue of climate warming [START_REF] Peters | Carbon Dioxide Emissions Continue to Grow amidst Slowly Emerging Climate Policies[END_REF] . Controlling of the consumption of traditional fossil-based transportation fuels and chemicals is one of the main ways to reduce CO2 emissions and achieve "carbon neutrality" [START_REF] Peter | Reduction of CO2 to Chemicals and Fuels: A Solution to Global Warming and Energy Crisis[END_REF][START_REF] Shahid | Biofuels and Biorefineries: Development, Application and Future Perspectives Emphasizing the Environmental and Economic Aspects[END_REF] . Although transportation fuels may be gradually replaced by more sustainable energy sources like wind, solar and hydro technology, chemicals should still rely on carbon-based resources [START_REF] Ennaert | Potential and Challenges of Zeolite Chemistry in the Catalytic Conversion of Biomass[END_REF] . In this sense, increasingly research attentions focus on the valorization and exploration of renewable carbon-based sources such as biomass to chemicals [START_REF] Shahid | Biofuels and Biorefineries: Development, Application and Future Perspectives Emphasizing the Environmental and Economic Aspects[END_REF][START_REF] Taarning | Zeolite-Catalyzed Biomass Conversion to Fuels and Chemicals[END_REF] .

Methanol is an essential molecule for biomass conversion into chemicals [START_REF] Li | Exergy Analysis of Renewable Light Olefin Production System via Biomass Gasification and Methanol Synthesis[END_REF] . On one hand, methanol can be easily manufactured via biomass gasification [START_REF] Santos | Biomass-Derived Syngas Production via Gasification Process and Its Catalytic Conversion into Fuels by Fischer Tropsch Synthesis: A Review[END_REF] , and on the other hand, methanol can also be converted via dehydration to various chemicals such as dimethylether (DME) and light olefins [START_REF] Tian | Methanol to Olefins (MTO): From Fundamentals to Commercialization[END_REF] . For the latter process, zeolites (e. g. ZSM-5, SAPO-34, ZSM-22, ferrierite, etc.) play a dominant role due to the flexible and adjustable chemical composition (silicon-to-aluminum ratio), high hydrothermal stability and surface acidity [START_REF] Li | Comparative Study of MTO Conversion over SAPO-34, H-ZSM-5 and H-ZSM-22: Correlating Catalytic Performance and Reaction Mechanism to Zeolite Topology[END_REF][START_REF] Catizzone | New Synthesis Routes and Catalytic Applications of Ferrierite Crystals. Part 2: The Effect of OSDA Type on Zeolite Properties and Catalysis[END_REF] . However, the catalytic performance of the zeolites is always weakened by coke formation, which is chiefly due to the undesired nature, distribution and strength of the acid sites [START_REF] Catizzone | Catalytic Application of Ferrierite Nanocrystals in Vapour-Phase Dehydration of Methanol to Dimethyl Ether[END_REF][START_REF] Migliori | New Insights about Coke Deposition in Methanol-to-DME Reaction over MOR-, MFI-and FER-Type Zeolites[END_REF] . Therefore, it is of vital importance to find a solution towards improving the performance of zeolite catalysts by tuning their acidity in methanol dehydration process [START_REF] Busca | Acid Catalysts in Industrial Hydrocarbon Chemistry[END_REF] .

The main acidity of zeolites resides in the presence of Brønsted Acid Sites (BAS), however the hydrophobicity of the zeolite does not rely only on them and silanol networks play a crucial role in coke deposition being also more or less polar bonds [START_REF] Medeiros-Costa | Silanol Defect Engineering and Healing in Zeolites: Opportunities to Fine-Tune Their Properties and Performances[END_REF] . This was recently highlighted in a study relating vapor adsorption capacities of water and methanol in zeolites to the hydroxyl concentration measured with [START_REF] Feng | Surface Dealumination of Micro-Sized ZSM-5 for Improving Propylene Selectivity and Catalyst Lifetime in Methanol to Propylene (MTP) Reaction[END_REF] Si NMR and IR spectroscopy [START_REF] Lions | The Pivotal Role of Critical Hydroxyl Concentration in Si-Rich Zeolites for Switching Vapor Adsorption[END_REF] . Thus, the passivation of zeolite surface is a promising way in tuning properties of already functional catalysts in the industry like ZSM-5 zeolites especially when polar molecules are involved.

To adjust the surface acidity and hydrophobicity, several techniques have been applied on several zeolites within "hybrid" (Red-Ox/Acid) catalyst toward improving their performance and stability for sustainable processes [START_REF] Li | Applications of Zeolites in Sustainable Chemistry[END_REF][START_REF] Bonura | Interaction Effects between CuO-ZnO-ZrO2 Methanol Phase and Zeolite Surface Affecting Stability of Hybrid Systems during One-Step CO2 Hydrogenation to DME[END_REF] . One typical example is the epitaxial growth applied for passivation of zeolite surfaces, thus, to control the surface acidity and protect metallic sites promoting the coupling with the acid phase in a "hybrid catalysts" [START_REF] Wu | Preparation of Silicalite-1@Pt/Alumina Core-Shell Catalyst for Shape-Selective Hydrogenation of Xylene Isomers[END_REF][START_REF] Yang | Facile Synthesis of H-Type Zeolite Shell on a Silica Substrate for Tandem Catalysis[END_REF] . Enlighted by such an example, depositing a pure silica MFI zeolite (Silicalite-1) shell on the surface of the ZSM-5 zeolite core is a plausible way to passivate the undesired acidity within the ZSM-5 zeolite core [START_REF] Van Vu | Selective Formation of Para-Xylene over H-ZSM-5 Coated with Polycrystalline Silicalite Crystals[END_REF][START_REF] Vu | Catalytic Activities and Structures of Silicalite-1/H-ZSM-5 Zeolite Composites[END_REF][START_REF] Van Vu | Morphology Control of Silicalite/HZSM-5 Composite Catalysts for the Formation of Para-Xylene[END_REF] and to modify the acidity and tailor the catalysts' properties [START_REF] Li | Synthesis of SAPO-34@ZSM-5 and SAPO-34@Silicalite-1 Core-Shell Zeolite Composites for Ethanol Dehydration[END_REF][START_REF] Bouizi | Beads Comprising a Hierarchical Porous Core and a Microporous Shell[END_REF][START_REF] Fan | Synthesis of ZSM-5/SAPO-11 Composite and Its Application in FCC Gasoline Hydro-Upgrading Catalyst[END_REF][START_REF] Zheng | Hierarchical Core-Shell Zeolite Composite ZSM-5@SAPO-34 Fabricated by Using ZSM-5 as the Nutrients for the Growth of SAPO-34[END_REF][START_REF] Zhang | Synthesis of Core-Shell ZSM-5@meso-SAPO-34 Composite and Its Application in Methanol to Aromatics[END_REF][START_REF] Razavian | Synthesis and Application of ZSM-5/SAPO-34 and SAPO-34/ZSM-5 Composite Systems for Propylene Yield Enhancement in Propane Dehydrogenation Process[END_REF] . Moreover, various other techniques have been tested and described in literature to reach the goal of passivating surface acidity. Surface dealumination of a nano-sized ZSM-5 zeolite carried out before the organic template removal, allowed to prolong the lifetime of catalyst employed in the reaction of methanol to propylene [START_REF] Feng | Surface Dealumination of Micro-Sized ZSM-5 for Improving Propylene Selectivity and Catalyst Lifetime in Methanol to Propylene (MTP) Reaction[END_REF] . Recently, it was also showed that reversing the external surface of ZSM-5 zeolite by positively charged hexadecyltrimethylammonium??? (HDTMA) allowed a selectively deposit of phosphorus on the external surface and pore entrance, thus leading to improved para-selectivity in the alkylation of toluene with methanol [START_REF] Yi | Catalytic Performance of Modified ZSM-5 Designed with Selectively Passivated External Surface Acidity by Phosphorus[END_REF] . Additionally, chemical liquid deposition (CLD) and chemical vapor deposition (CVD) of TEOS have been successfully employed with the purpose of passivating surface acidity of zeolites [START_REF] Mesa | Ferrierite Zeolite Passivation and Its Catalytic Application in Toluene Disproportionation[END_REF][START_REF] Zhu | Shape-Selective Disproportionation of Ethylbenzene to Para-Diethylbenzene over ZSM-5 Modified by Chemical Liquid Deposition and MgO[END_REF][START_REF] Lv | Surface-Passivated Hierarchically Structured ZSM5 Zeolites: High-Performance Shape-Selective Catalysts for Para-Xylene Production[END_REF][START_REF] Losch | Impact of External Surface Passivation of Nano-ZSM-5 Zeolites in the Methanol-to-Olefins Reaction[END_REF] .

The classical strategy for core-shell catalyst includes a two-step procedure, involving the core preparation and the shell growth; the coupling of Silicalite-1 on a ZSM-5 zeolite is the most used strategy. The thickness and morphology of Silicalite-1 shells are affected by the Si/Al ratio [START_REF] Van Vu | Selective Formation of Para-Xylene over H-ZSM-5 Coated with Polycrystalline Silicalite Crystals[END_REF] and/or crystal size of the ZSM-5 core [START_REF] Vu | Catalytic Activities and Structures of Silicalite-1/H-ZSM-5 Zeolite Composites[END_REF] and the coating procedure applied. The morphology of the core-shell zeolites is also dependent on the silica sources and structure-directing agent (SDA) used for preparing the precursor mixtures [START_REF] Van Vu | Morphology Control of Silicalite/HZSM-5 Composite Catalysts for the Formation of Para-Xylene[END_REF] .

Improved stability for ZSM-5/Silicalite-1 core-shell catalyst containing Mo in methane de-hydro-aromatization was reported; the core-shell catalyst exhibited an excellent shape selectivity without lowering the conversion significantly as a consequence of the reduced acidity [START_REF] Jin | Methane Dehydroaromatization by Mo-Supported MFI-Type Zeolite with Core-Shell Structure[END_REF] . The advantage of tuning the surface acidity of the core-shell catalysts in methanol-to-hydrocarbon reactions and pyrolysis was reported as well [START_REF] Goodarzi | Synthesis of Mesoporous ZSM-5 Zeolite Encapsulated in an Ultrathin Protective Shell of Silicalite-1 for MTH Conversion[END_REF]3738 . Other examples for ZSM-5 zeolites coated with a layer of Silicalite-1 were reported and employed in various applications [START_REF] Zheng | Structural Features of Core-Shell Zeolite-Zeolite Composite and Its Performance for Methanol Conversion into Gasoline and Diesel[END_REF] such as methanol conversion into gasoline and diesel [START_REF] Zheng | Structural Features of Core-Shell Zeolite-Zeolite Composite and Its Performance for Methanol Conversion into Gasoline and Diesel[END_REF] , ketonization and cracking reactions [START_REF] Ghorbanpour | Epitaxial Growth of ZSM-5 @ Silicalite-1 : Passivated Surface Acidity[END_REF] and alkylation of toluene [START_REF] Van Vu | Selective Formation of Para-Xylene over H-ZSM-5 Coated with Polycrystalline Silicalite Crystals[END_REF][START_REF] Vu | Catalytic Activities and Structures of Silicalite-1/H-ZSM-5 Zeolite Composites[END_REF][START_REF] Van Vu | Morphology Control of Silicalite/HZSM-5 Composite Catalysts for the Formation of Para-Xylene[END_REF][START_REF] Deng | Synthesis of HZSM-5@silicalite-1 Core-Shell Composite and Its Catalytic Application in the Generation of p-Xylene by Methylation of Toluene with Methyl Bromide[END_REF][START_REF] Li | Core-Shell HZSM-5@silicalite-1 Composite: Controllable Synthesis and Catalytic Performance in Alkylation of Toluene with Methanol[END_REF] . However, the Si/Al ratio in ZSM-5 core used was relatively high, ranging from 25 to more than 100, which hinders to broaden the application of the core-shell catalyst is the acidity of the zeolitic core.

In this paper, we report the preparation of novel catalysts with a ZSM-5 core with a low Si/Al ratio passivated with a single and multi-layer Silicalite-1. The novel catalysts with high aluminum content of the core and high number of external acid sites were tested in methanol dehydration reaction.

EXPERIMENTAL

Preparation of Core-Shell Zeolite Catalysts

A ZSM-5 zeolite (Si/Al=11 in the gel) was prepared under hydrothermal conditions [START_REF] Migliori | Methanol to Dimethylether on H-MFI Catalyst: The Influence of the Si/Al Ratio on Kinetic Parameters[END_REF] starting from a gel with the following molar composition: 0.08 Na2O-0.08 TPABr-0.045Al2O3-1 SiO2-20 H2O. Briefly 0,56 g of sodium hydroxide (NaOH), 2,82 g of sodium aluminate (NaAlO2) and 7.1 g of tetrapropylammonium bromide (TPABr) were dissolved in 119.6 g of distilled water. Finally, 20 g of precipitated silica (ADD TYPE ???) was added. The resultant gel was stirred for 1 h at room temperature, then transferred in a PTFE-lined stainless-steel autoclave and kept in a static oven at 170°C for 7 days. The obtained sample was washed with distillate water and calcinated at 550°C to eliminate the structural organic template (SDA). The acidic form of the samples was obtained after two cycles (2 h each at 80°C) of ionic exchange with NH4Cl (1 M) and a subsequent calcination at 550°C. The parent zeolite catalyst labeled as ZSM-5_P was also used as a starting material for the following passivation treatments with Silicalite-1.

Two catalysts with passivated surface acidity were synthesized by growth of Sillicalite-1 on the parent zeolite sample (ZSM-5_P) using a single-step or doublestep deposition. 5 g of ZSM-5 crystals in H + -form were immersed in 10 g of Silicalite-1 precursor mixture prepared by mixing tetraethyl orthosilicate (TEOS), tetrapropylammonium hydroxide (TPAOH), and deionized water. The precursor mixture with the following molar was obtained: 2 SiO2: 0.5 TPAOH: 8 EtOH: 120 H2O [START_REF] Vu | Catalytic Activities and Structures of Silicalite-1/H-ZSM-5 Zeolite Composites[END_REF] . The hydrothermal synthesis was performed at 180°C for 24h using a tumbling oven, and the as-prepared materials after purification was calcined at 550°C (ramp: 2°C/min, duration time: 8 h, condition: static air) (named as single-Silicalite-1 deposition step catalyst: ZSM-5_X). After purification and calcination, a part of ZSM-5_X crystals was used to repeat the synthesis of the Silicalite-1 shell, in a new synthesis gel, in order to increase the Silicalite-1 thickness and to obtain a better passivation performance (named as double-Silicalite-1 deposition step catalyst ZSM-5_XX).

Characterization of the catalysts

The crystallinity of the samples was determined by a Miniflex600 (Rigaku, Japan) diffractometer (λ Cu = 1.540560 Å, 40 kV, 15 mA); the X-ray diffraction patterns were recorded in the 2 range 5-40° (step: 0.01°; scanning rate: 1°/min).

The chemical composition of the samples was characterized using a GBC 932AA atomic absorption spectrometer (AAS, GCB Scientific Equipment, Australia).

Electron microscopy imaging and Energy Dispersive X-Ray Spectroscopy (EDS)

were performed using a JEOL F200 transmission electron microscope (TEM) operated at 200kV equipped with a Gatan RIO16 camera and a JEOL Centurio EDS detector.

The N2 physisorption measurements of the samples were carried out using an ASAP 2020 porosimeter (Micromeritics, USA) at 77 K. Specific surface areas and micropore volumes were calculated using the BET and t-plot methods, respectively [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF] .

NH3 temperature-programmed desorption measurements (NH3-TPD) of zeolites [START_REF] Catizzone | The Effect of FER Zeolite Acid Sites in Methanol-to-Dimethyl-Ether Catalytic Dehydration[END_REF] were performed by a TPDRO1100 (Thermo Scientific, USA) equipped with a TCD detector, according to the following procedure. 100 mg of dried sample were loaded in a linear quartz micro-reactor (i.d., 4 mm; l., 200 mm) and pre-treated at 300 °C in helium flow of 20 ml/min. Then temperature was lowered to 150 °C and the sample was saturated with a stream of NH3/He (10% v/v) flowing at 20 ml/min for 120 minutes. Afterward, physisorbed ammonia was removed at 150 °C using a helium flow until TCD-signal baseline stabilization. Ammonia desorption measurement was carried out in the temperature range of 100-700 °C with a heating rate of 10 °C/min using a helium flow rate of 20 ml/min.

The IR spectra of the samples were recorded using a Nicolet iS 10 FTIR spectrometer (Thermo Scientific, USA) equipped with a DTGS detector. The selfsupported samples (25 mg, disk) were initially outgassed at 10 -5 torr under heating (400°C for 2h, heating rate of 10 °C/min), and the spectra before and after pyridine (Py) delivery were recorded. FTIR spectra were measured at room temperature (r.t.) and 10 -5 -10 -4 Torr in the mid-infrared region (MIR: 4000-400 cm -1 ), with an optical resolution of 4cm -1 46,47 . The physisorbed Py was removed under degassing of the sample at 150°C and 10 -5 Torr for 60min before spectrum acquisition [START_REF] Zholobenko | Probing the Acid Sites of Zeolites with Pyridine: Quantitative AGIR Measurements of the Molar Absorption Coefficients[END_REF] . The concentration of the Brønsted and Lewis acid sites was calculated via integration of the peaks at 1545 cm -1 and ⁓1454 cm -1 , respectively [START_REF] Gould | Quantification of Acid Site Densities on Zeolites in the Presence of Solvents via Determination of Extinction Coefficients of Adsorbed Pyridine[END_REF][START_REF] Bordiga | Probing Zeolites by Vibrational Spectroscopies[END_REF] . The measurement was performed on three independent samples and data were reported as an average standard deviation.

Catalytic tests

140 mg of catalysts (pellet, 300-500m) were tested in a U-shaped quartz packed bed reactor (ID = 15mm, L = 40mm) at 140-240°C and atmospheric pressure with a weight hourly space velocity (WHSV) of 4gMeOH•(gcat•h) -1 using a mixture of methanol (0.06 mol/mol) and nitrogen as carrier (60 STP ml/min) [START_REF] Aloise | Desilicated ZSM-5 Zeolite: Catalytic Performances Assessment in Methanol to DME Dehydration[END_REF] , after 2h pretreatment at 240°C in N2 flow. Temperature and time for the pretreatment of the samples were established based on the TG results for the catalysts in H + form;

the temperature for removal of water was identified.

A GC-FID (Agilent 7890 A) equipped with a J&W 125-1032 column was used to measure the products [START_REF] Aloise | Desilicated ZSM-5 Zeolite: Catalytic Performances Assessment in Methanol to DME Dehydration[END_REF] . Methanol conversion ( ) and DME selectivity ( ) were calculated according to eq. 1 and 2, considering methanol (MeOH) and DME molar flow rate entering (in) or leaving the reactor (out):

(

(2)

Coke Analysis

The amount of deposited coke on the used catalysts was measured by thermogravimetric analysis (TGA) using a TA Instruments SDT 650; the weight loss in the range 250-850°C (heating rate 10°C/min) was measured [START_REF] Migliori | New Insights about Coke Deposition in Methanol-to-DME Reaction over MOR-, MFI-and FER-Type Zeolites[END_REF] . The soluble coke species were detected via GC-MS (Agilent 7820A, MSD 5977E) analysis. Prior to the test, HF (40%) was used for dissolving the spent catalysts; then, dichloromethane was used as organic phase to extract the coke species [START_REF] Aloise | Desilicated ZSM-5 Zeolite: Catalytic Performances Assessment in Methanol to DME Dehydration[END_REF] .

RESULTS AND DISCUSSION

Physical and chemical properties of samples

The X-ray patterns of the parent ZSM-5 and passivated catalysts contain the characteristic Bragg peaks for the MFI type zeolites (Figure 1); no other phases were observed. The intensity of the (120) and (053) peaks at 9.851 and 29.904° 2Theta slightly decreased for the samples with passivated surface acidity.

Conversely, the intensity of the (011) peak at 7.935° slightly increased. The latter observation might indicate a preferential growth of the Silicalite-1 on the (011) plane. Conversely, the intensity of the (120) and (053) peaks decreased, which is in line with the formation of an amorphous silica shell on the surface of the parent ZSM-5 zeolite.

FIGURE 1 HERE

The chemical composition of the samples is summarized in Table 1; the Si/Al ratio increases with the increasing of Silicalite-1 layer thickness. The amount of Silicalite-1 shell was estimated to be 12 wt. % and 31 wt. % in the single and double-deposition step of Silicalite-1, respectively [START_REF] Jin | Methane Dehydroaromatization by Mo-Supported MFI-Type Zeolite with Core-Shell Structure[END_REF] . The AA analyses were also performed of the mother liquor after the solid separation and in all cases, the presence of aluminum was not detected.

TABLE 1 HERE

All samples present a mixed Type I/IV isotherms with H4 hysteresis at 0.45 P/P 0 (Figure 2), typical of aggregated crystals containing textural mesopores [START_REF] Thommes | Physisorption of Gases, with Special Reference to the Evaluation of Surface Area and Pore Size Distribution (IUPAC Technical Report)[END_REF] .

The parent zeolite ZSM-5_P showed similar porosity to other MFI zeolites reported before [START_REF] Bae | Evaluation of the BET Method for Determining Surface Areas of MOFs and Zeolites That Contain Ultra-Micropores[END_REF] . The BET surface area (SBET) of the ZSM-5_X sample decreased by 14 %, with respect to the parent sample (Table 1), which is in line with other published results [START_REF] Li | Coating Mesoporous ZSM-5 by Thin Microporous Silicalite-1 Shell: Formation of Core/Shell Structure, Improved Hydrothermal Stability and Outstanding Catalytic Performance[END_REF] .

FIGURE 2 HERE

A similar trend was observed for the microporous area (Smicro) and external surface area (Sext) of ZSM-5_X. BET surface area (SBET), microporous area (Smicro) and external surface area (Sext) of double-Silicalite-1 deposited sample ZSM-5_XX was higher than that of the sample with only one Silicalite-1 deposition step.

TEM observations of the of the parent ZSM-5 sample reveal a bimodal particle size distribution. Two types of agglomerates are observed, consisting, on the one hand, of crystals of 100 nm maximum (Figure 3A) and, on the other hand, of larger crystals in the form of rods (thickness greater than 200 nm and length greater than 1 micrometer). In both cases, the shape of the crystals is well defined, and their surface is free of any coating (Figure 3B).

After the first passivation step, it is possible to observe the presence of amorphous material surrounding the two types of agglomerates (Figure 4A).

Individually, the surface of the crystals is also covered, at least partially, by a thin amorphous layer (Figure 4B).

FIGURE 4 HERE

After the second passivation step, the ZSM-5 surface is covered by a thicker layer (Figure 5A). Within this layer, crystalline domains representative for MFI type zeolites can be seen (Figure 5B).

FIGURE 5 HERE

The NH3-TPD profiles of the samples (Figure 6) exhibit peaks at different temperatures: (l) is the low temperature peak (i.e. below 300°C), (m) is the medium temperature peak (below 500°C) and two peaks are also present at temperature higher than 550°C. In order to assess the acidity of the samples, due to the partial overlapping of the peaks, all of them were considered for the overall curve deconvolution. Moreover, since the peaks at temperature above 550°C are most likely associated with silanols dihydroxylation [START_REF] Babu | Active Centres over HZSMS Zeolites I. Xylene Isomerization[END_REF] , their contribution was not included in the total acidity determination (Table 2). The NH3 adsorption of the ZSM-5_X sample in comparison to the parent ZSM-5_P decreased by 26%, and this is in agreement with the evidence of the formation of an amorphous silica layer on the core [START_REF] Li | Coating Mesoporous ZSM-5 by Thin Microporous Silicalite-1 Shell: Formation of Core/Shell Structure, Improved Hydrothermal Stability and Outstanding Catalytic Performance[END_REF] even though no detectable in the XRD, reducing the accessibility of the structure by the probe molecule. Furthermore, the total NH3 adsorption measured for the double-Silicalite-1 deposited (ZSM-5_XX) zeolite is lower than that of the parent ZSM-5_P but higher than that of the ZSM-5_X sample. A similar trend was observed for the medium temperature peak (m), and the (l) and (h) peaks decreased for the samples after a single and double Silicalite-1 deposition step (Table 2).

FIGURE 6 HERE TABLE 2 HERE

The FT-IR spectra of the parent and catalysts with passivated surface acidity using Pyridine (Figure 7) indicate a stepwise decrease of the Brønsted and Lewis acidity for both ZSM-5_X and ZSM-5_XX samples, which correlate linearly with the Si/Al ration of the catalysts (Table 2). The pyridine was used as a probe molecule, and the spectra were recorded after treatment of the samples at 150°C [START_REF] Zholobenko | Probing the Acid Sites of Zeolites with Pyridine: Quantitative AGIR Measurements of the Molar Absorption Coefficients[END_REF] . The FT-IR results for samples ZSM-5_P and ZSM-5_X are in line with the NH3-TPD results whilst 23% difference was found for sample ZSM-5_XX. This difference could be probably due to the different size of the probes used, i.e., pyridine being larger failed to reach all acid sites. This result are in agreement with previous reports [START_REF] Li | Coating Mesoporous ZSM-5 by Thin Microporous Silicalite-1 Shell: Formation of Core/Shell Structure, Improved Hydrothermal Stability and Outstanding Catalytic Performance[END_REF] and a good linear correlation (see Supplementary Information) between the Al content (Table 1) and acidity the of the catalyst from FT-IR is found. Therefore, the data from the Pyridine adsorption measurements were used in the discussion.

FIGURE 7 HERE

Catalytic tests

The methanol conversion for all catalysts was found to be improved with raising the temperature from 140 to 240°C, approaching the equilibrium at 240 °C (Figure 8). The parent catalyst ZSM-5_P showed the highest conversion at all temperatures. This is attributed to the highest acidity of the parent ZSM-5_P catalyst. While the single-Silicalite-1 deposited sample (sample ZSM-5_X) with similar acidity to the parent catalyst according to the FTIR showed lower conversion in the entire temperature range. The double-Silicalite-1 deposited catalyst (sample ZSM-5-XX) favorably impacts the methanol conversion compared to the ZSM-5_X sample, although the acidity was markedly reduced.

FIGURE 8 HERE

The selectivity was equal to 1 for all samples in the range 160-200°C. At 220 and 240°C, the double-Silicalite-1 deposited catalyst (ZSM-5_XX) exhibited the highest selectivity of 98.4 and 96.9 %, respectively; a more pronounced decrease of the selectivity was detected for the single Silicalite-1 layered catalyst (ZSM-5-X). It seems that the observed trends in the conversion and selectivity are not in accordance with the acidity of the catalysts and are more dependent on their textural properties. Compared to the ZSM-5_P and ZSM-5_XX catalysts, the BET surface area, micropore area, and external surface areas are decreased for ZSM-5_X catalyst. This sample also showed higher silica content according to the chemical analysis and the arrangement of this layer in form of an amorphous silica shell was supported by the partial decrease of the Bragg peaks with (hkl) of ( 120) and (053) (Figure 1). Therefore, the reduced conversion for ZSM-5_X could be attributed to the surface properties of the samples; the amorphous silica shell partially blocked the ZSM-5_X and was restored after the growth of the second shell. The lower selectivity showed by the ZSM-5_X catalyst, with respect to the ZSM-5_P and ZSM-5_XX catalysts, could indicate the increased pore tortuosity at the pore mouth, induced by the presence of amorphous silica, leading to an enhanced residence time of the formed DME within the micropores, in the presence of acidic sites, and also to the formation of olefins. This is confirmed by the detection of C2-C3 olefins as a function of temperature, as presented in Figure 9.

FIGURE 9 HERE

It clearly appears that no olefin signal was detected at temperatures lower than 220°C, whilst the ZSM-5_X promoted more olefins than the parent ZSM-5_P catalyst. On the contrary, this effect was significantly reduced in the case of the double-Silicalite-1 deposited catalyst (ZSM-5_XX), which is in accordance with the recovered textural properties of the sample and reduced acidity.

Another interesting observation is the acid sites efficiency based on the average/apparent Turn Over Frequency (TOF), calculated far from the equilibrium conditions at 160° and 180°C (Figure 10):

where the ratio WHSV/MWMeOH is the MeOH hourly molar flow rate per gram of catalyst [μmol•(gcat•h) -1 ], xMeOH is the observed MeOH conversion, and total AS is the Brønsted acid sites concentration (μmol•gcat -1 ) determined from FTIR data (Table 2). The Brønsted acid sites are of vital importance in dehydration reactions.

FIGURE 10 HERE

In summary, the double-Silicalite-1 deposited catalyst (ZSM-5_XX) showed the best performance in terms of acid sites efficiency in comparison to the parent ZSM-5_P and single-Silicalite-1 deposited catalyst ZSM-5_X at 180°C.

Coke Analysis

TGA analyses were performed on used parent and catalysts covered with Silicalite-1 after 5 h reaction. The DTG curves contain two broad peaks at 321-357°C (low-temperature region, LT) and at 549-563°C (high-temperature region, HT), indicating the presence of coke on the spent catalysts [START_REF] Aloise | Desilicated ZSM-5 Zeolite: Catalytic Performances Assessment in Methanol to DME Dehydration[END_REF] . The spent single-Silicalite-1 deposited catalyst (ZSM_5_X) showed the highest coke formation (Table 3), while the spent double-Silicalite-1 deposited catalyst (ZSM-5_XX) contained the lowest amount of coke.

TABLE 3 HERE

GC-MS analysis of the coke species extracted from the spent parent, and catalysts with passivated surface acidity revealed the presence of pentamethyl benzene and hexamethyl benzene (Figure 11), which are the typical coke species found on the external surface of spent catalyst used for the dehydration of methanol to DME [START_REF] Migliori | New Insights about Coke Deposition in Methanol-to-DME Reaction over MOR-, MFI-and FER-Type Zeolites[END_REF] .

FIGURE 11 HERE

The area of the peaks associated with pentamethyl-benzene and hexamethylbenzene (Figure 11) correlated well with the total weight loss determined by TGA (correlation not shown), thus suggesting that the weight loss could be related to the soluble coke species coherent with the relatively low reaction temperatures.

Moreover, the ZSM-5_X catalyst has shown the presence of 1,2,4,5tetramethylbenzene, while the latter was not shown for the ZSM-5_P and ZSM-5_XX catalysts, in line with the assumed increased tortuosity for the ZSM-5_X sample.

CONCLUSIONS

The goal of passivating the surface acidity of a high Al containing ZSM-5 zeolite by single-and double-layer Silicalite-1 deposition step has been successfully achieved. The obtained samples were used for the reaction of methanol dehydration to DME. Compared to the parent ZSM-5 zeolite, the conversion and selectivity of the single-Silicalite-1 layered catalyst were found to decrease while the amount of coke increased with respect to the uncovered ZSM-5. The formation of an amorphous silica layer after the first growth cycle ended up in a low conversion and selectivity of the ZSM-5_X catalyst. On the contrary, catalytic results demonstrated that depositing a second of Silicalite-1 layer could positively contribute to the catalyst performance. Reduction in surface acidity, mainly responsible for coke formation, improved the catalyst efficiency with significant reduction of coke formation, mainly poly-methyl benzenes, on the external surface of the spent catalysts. In addition, calculation of Turn Over Frequency, calculated using Brønsted acid sites, confirmed a comparable efficiency of the double-layered passivated catalysts and the parent zeolite.

FIGURES CAPTIONSFigure 1 . 5 Figure 2 .

 152 FIGURES CAPTIONS

Figure 3 .

 3 Figure 3. TEM pictures of parent zeolite (ZSM-5_P) showing the clean edges of (A,

Figure 4 .

 4 Figure 4. TEM pictures of single-deposition step Silicalite-1 layered catalyst ZSM-

Figure 5 .

 5 Figure 5. TEM pictures of double-deposition step Silicalite-1 layered catalyst ZSM-

Figure 6 .

 6 Figure 6. NH3-TPD profiles of parent (ZSM-5_P), single-step Silicalite-1 layered

Figure 7 .

 7 Figure 7. FTIR spectra on the parent ZSM-5_P, single-Silicalite-1 layer catalyst

Figure 8 .

 8 Figure 8. Methanol conversion and selectivity of parent (ZSM-5_P), single-step

Figure 9 .Figure 10 .

 910 Figure 9. Olefins formation as a function of temperature on parent (ZSM-5_P),

Figure 11 .

 11 Figure 11. GC-MS analysis of the spent parent (ZSM-5_P), single-step Silicalite-1

Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7

 234567 Figure 2

Figure 12

 12 Figure9

Table 1 .

 1 Textural properties of parent (ZSM-5_P), single-step Silicalite-1 layered

	TABLES CAPTIONS
	catalyst (ZSM-5_X) and double-step Silicalite-1 layered catalyst (ZSM-5_XX)
	determined by N2 physisorption analysis at -196°C.

Table 2 .

 2 Acidity

	of parent (ZSM-5_P), single-step Silicalite-1 layered catalyst
	(ZSM-5_X) and double-step Silicalite-1 layered catalyst (ZSM-5_XX) measured by
	NH3-TPD analysis and FTIR using pyridine as a probe molecule. (Data are ±
	Standard deviation)

Table 3 .

 3 Coke formation on used parent (ZSM-5_P), single-step Silicalite-1

	layered catalyst (ZSM-5_X) and double-step Silicalite-1 layered catalyst (ZSM-
	5_XX) after 5h time-on-stream.

Table 1

 1 Calculated by the multipoint BET method in the Rouquerol p/p 0 range; b Calculated by the t-plot method; c Calculated at p/p 0

		Si/Albulk	SBET a	Smicro b	Sext b	Vp c	Vmicro b
	Catalyst
		mol/mol	(m 2 /g)	(m 2 /g)	(m 2 /g)	(cm 3 /g)	(cm 3 /g)
	ZSM-5_P	15.4	404	310	94.3	0.21	0.12
	ZSM-5_P_X	17.6	349	267	80.0	0.17	0.10
	ZSM-5_P_XX	27.1	389	293	96.0	0.20	0.11
	0.95

a a l and m are low and medium temperature desorption peaks respectively. Values into parenthesis (°C); b B: Brønsted acid sites (IMECB= 1.02 cm/μmol); L: Lewis acid sites (IMECL= 0.89 cm/μmol)

Table 3

 3

	Catalyst	mg COKE/g Cat	mg COKE /g Formed DME
	ZSM-5_P	31	0.8
	ZAM-5_X	39	1.3
	ZSM-5_XX	22	0.7

ACKNOWLEDGMENTS

Authors gratefully acknowledge the "Ministero degli Affari Esteri e della Cooperazione Internazionale" (MAECI) of Italy and "Ministry of Science and Technology of the People's Republic of China" (MOST) for the financial support of project "B2CLIF -Biowaste to Chemicals and LIquid Fuels", cofunded in the framework of a bilateral agreement between MAECI and MOST.