Robust H∞ Network Observer-Based Attack-Tolerant Path Tracking Control of Autonomous Ground Vehicle

In this study, a robust $H_{\infty }$ network observer-based attack-tolerant path tracking control design is proposed for the autonomous ground vehicle (AGV) under the effect of external disturbance, measurement noise and actuator/sensor attack signals. At first, a more practical AGV system is applied to describe the interaction among the longitudinal speed, lateral speed and yaw rate. Based on Controller Area Network (CAN), the information of local AGV is transmitted to remote control center through wireless channel and then the control command can be calculated from remote control center. To avoid the corruption of actuator/sensor attack signal from insecure CAN, two novel smoothed signal models are introduced to describe these attack signals and are embedded with the AGV dynamics system as an augmented system. Subsequently these attack signals can be simultaneously estimated with the AGV system state by the conventional Luenberger-type observer of the augmented system. By using the estimated state and attack signals, a robust $H_{\infty }$ network observer-based attack-tolerant path tracking controller is constructed to attenuate the effect of unknown disturbance on the energy of path tracking error and eliminate the influence of attacks signals. With the help of convex Lyapunov function, the design conditions of robust $H_{\infty }$ network observer-based attack-tolerant path tracking control design for AGV are derived in terms of a set of nonlinear difference inequalities. To reduce the difficulties in solving these nonlinear difference inequalities, Takagi-Sugeno fuzzy interpolation method is applied to approximate the nonlinear AGV system and the design can be simplified to a set of LMIs, which can be easily solved via LMI TOOLBOX in MATLAB. A double lane change task of AGV in CAN is provided as a simulation example to illustrate the design procedure and validate the effectiveness of proposed design method in comparison with the conventional steering control method.


I. INTRODUCTION
In the past two decades, the autonomous ground vehicle (AGV) plays an important role in the intelligent transportation system [1]- [3]. In general, the AGV is self-controlled based on the predefined navigation trajectory and perceives environmental information. Compared to the human-controlled vehicle, which may have improper decisions during the maneuvering process, the AGV provides more advantages such as the optimal fuel consumption, road The associate editor coordinating the review of this manuscript and approving it for publication was Dazhong Ma . safety, etc. Conventionally, the navigation process of AGV can be separated as three parts including: (i) environmental information gathering [4], (ii) decision making and path planning [5], and (iii) path tracking control. These threes parts have got a lot of attentions in recent years whether in academic research field or in industrial development.
For the above mentioned design process, the path tracking control (i.e., the steering control) is a crucial issue. Briefly, it aims to design an appropriate steering angle for AGV to achieve the desired lateral velocity and thus generate an appropriate motion such as lane change. The conventional control methods of AGV on path tracking include nested PID steering control [6] and fuzzy adaptive PID control [7]. Further, with the utilization of modern control technology, there are many novel steering control methods such as output feedback control [8], fuzzy observer-based control [9], fuzzy output feedback control [10], etc. Even there are fruitful results about the steering control of AGV, it worths to point out that the longitudinal velocity is not well considered in the existing studies. Generally speaking, the longitudinal velocity will vary depending on the design purpose during the cruise and thus it will change the nonlinear system characteristic of AGV.
Recently, with the advance of communication technology, the vehicle-to-everything (V2X) with Controller Area Network (CAN) becomes a hot topic due to it's broad applications in future smart city [11]. By connecting the local AGV system with a remote computing center, the remote computing center can utilize the local environmental information of AGV and the global traffic information to design a more suitable path tracking trajectory with the corresponding steering control strategy. However, due to the uncertain quality of service (QoS) of wireless channel, two major issues (i) networked-induced delay [12] and (ii) packet dropout [13] have to be considered during the design. Thus, even the networked-based AGV structure is more appealing to the designer, it also brings some difficulties for the control design. Up to now, there are few studies to address the steering control of networked-based AGV. A networked-based robust path following control strategy design with the global positioning system (GPS) is investigated in [14]. The steering control over CAN with the consideration of time-varying delay is addressed in [15]. The model predictive trajectory tracking control design with random delay of AGV is developed in [16].
Other than the networked-induced effects (i.e., delay and data dropout), the information security in CAN is another crucial issue to be considered [17]- [19]. For example, once the control unit in the AGV plant or the remote control center is infected, the malicious adversary may send attack signal to deteriorate the control/estimation performance via communication channel [19]. Even some security protocols are developed to enhance the data confidentiality, the attack signal compensation should be further investigated from the view point of control design. In general, for the fault-tolerant control (FTC), it aims to design an observer to estimate the fault signals and the controller will use estimated fault signal for active fault compensation. Recently, the FTC has been widely applied to various fields. [20], [21]. Moreover, for the FTC of AGV, the fault-tolerant control (FTC) design based on disturbance observer for electric vehicle is provided to eliminate the actuator fault signal in [22]. Based on the residual theory, the sensor fault on front wheel steering angle measurement is effectively compensated for the electric vehicle in [23]. A model-based fault diagnosis technology is utilized to detect the actuator fault signal of AGV system in [24]. Further, under the effect of attack signal on sensor caused by wireless communication characteristics with the saturation effect, the AGV state estimation problem in CAN is investigated in [25]. Therein, the attack signal on sensor is augmented with AGV system to construct the descriptor system for the joint state/fault attack signal estimation. However, in the previous studies of FTC on AGV system, it usually involves algebraic equation constraints for the design of fault observer in [22] or a complicated SVM algorithm for fault diagnosis in [24].
Even the path tracking control of AGV has been widely addressed recently, the networked-based AGV steering control over CAN should be deeply investigated for the application in future smart city. The main reasons are discussed as follows: (i) In the most of studies, the model of longitudinal velocity is generally neglected and the longitudinal velocity in the resulting AGV system becomes a time-varying parameter or constant. However, in the real AGV system, the longitudinal velocity is also influenced by the lateral velocity and yaw rate and thus a more general model including the longitudinal velocity, the lateral velocity and the yaw rate should be used to completely describe the behavior of AGV system; (ii) Since the AGV information is transmitted via wireless channel in CAN, the transmitted data suffer not only wireless interference but also networkedinduced delay and packet dropout. An observer system should be developed to accurately estimate these data with the consideration of these effects for the observer-based control design; (iii) Even several security protocols are developed to address the data confidentiality [17]- [19], an active attack-tolerant path tracking control is more appealing for a networked AGV system to compensate the attack signals from the faulty actuator and faulty sensor. However, in the most of previous studies [22]- [25], only one of actuator attack signal or sensor attack signal is considered for the steering control design.
Motivated by the above discussion, the robust H ∞ network observer-based attack-tolerant path tracking control strategy for a networked-based AGV system is proposed with the consideration of external disturbance, measurement noise, actuator/sensor attack signal, networked-induced delay and packet dropout in future smart cities. Based on bicycle model, a complete AGV system including the lateral velocity, longitudinal velocity and yaw rate is constructed. Then, a CAN under the actuator/sensor attack signals is constructed to connect the local AGV system and remote control unit via wireless communication technique. To efficiently estimate the actuator/sensor attack signals, two smoothed signal models are utilized to describe the dynamic behavior of actuator/sensor attack signals. By augmenting the AGV state with two smoothed signal models, the conventional Luenbergertype observer can be applied for state/attack signal estimation in the remote control unit. Also, by using the estimation of state/attack signal with the desired path information, a robust H ∞ network observer-based attack-tolerant path tracking controller can be designed to achieve the path tracking task and to attenuate the effect of unavoidable external disturbance VOLUME 10, 2022 during the maneuvering process. Based on the Lyapunov stability theory and convex Lyapunov function, the design conditions can be derived in terms of a set of nonlinear difference inequalities. To deal with the difficulties in solving these nonlinear difference inequalities, the T-S fuzzy interpolation method is utilized to approximate the nonlinear AGV system by the interpolation of a set of local linearized AGV systems. After that, the design conditions of the robust H ∞ network observer-based attack-tolerant path tracking control strategy design is recast as a set of linear matrix inequalities (LMIs), which can be easily solved via MATLAB LMI TOOLBOX. A simulation example of double lane change task in city environment is provided to illustrate the effectiveness of proposed design method.
The contributions of this study are summarized as follows: (i) By including the model of longitudinal velocity in the resulting AGV system, the designer can directly control and maintain the longitudinal velocity to a desired value during the maneuvering process. Also, a networked-based AGV system in consideration of networked-induced effect and actuator/sensor attack signals is constructed to model the practical CAN structure. (ii) By using smoothed signal model to describe dynamic behavior of actuator/sensor attack signals, a conventional Luenberger observer can be used to accurately estimate the AGV system information and actuator/sensor attack signals simultaneously. Further, by using the estimated information, the robust H ∞ network observer-based attack-tolerant path tracking controller can be implemented to achieve the desired path tracking performance with active fault rejection capability. (iii) With the utilization of convex Lyapunov function, the design conditions of the robust H ∞ network observer-based attack-tolerant path tracking control design are derived in terms of a set of nonlinear difference inequalities. Moreover, by adopting T-S fuzzy interpolation method to approximate the nonlinear AGV system, the design conditions can be relaxed to a set of LMIs which can be easily solved for practical applications.
The study is organized as follows: In Section II, the modelling of AGV system with the corresponding CAN is introduced and the problem formulation is investigated. In Section III, the design conditions of robust H ∞ network observer-based attack tolerant path tracking control strategy design for nonlinear AGV system are transformed to equivalent nonlinear difference inequalities. In Section IV, with the help of T-S fuzzy interpolation method, the design conditions are relaxed to a set of solvable LMI conditions. In Section V, a simulation example of double lane change task is provided to illustrate the effectiveness of proposed control strategy. Some conclusion remarks are made in Section VI.
Notation: A T : the transpose of matrix A; eig(A): the set of the eigenvalues of matrix A; A > 0 (A ≥ 0): the positive-definite (semi positive-definite) matrix. 0 a×b : the zero matrix with dimension a × b, I n : the n-dimension identity matrix. col A: The column space of matrix A. E{·}: the expectation operator; l 2 : the function space which collects the finite energy functions. Matrices, if their dimensions are not specifically defined, are with appropriate dimensions for algebraic operation.

II. PRELIMINARY AND PROBLEM FORMULATION
In this section, the physical model of AGV system will be introduced. Next, under the concept of CAN, the AGV system is connected to a remote control unit with an observer to estimate the AGV information and attack signal. Then, the remote control unit can generate suitable path tracking control command with the utilization of estimated information. Besides, to attenuate the effect of unpredictable environmental noise, the robust H ∞ network observer-based attacktolerant path tracking control strategy is introduced.

A. PHYSICAL MODEL OF AUTONOMOUS GROUND VEHICLE
In this study, the physical model of front-wheel-driven AGV system is considered as a bicycle model (i.e., the vehicle is symmetric w.r.t. x − z plane) and the corresponding physical diagram of AGV system is shown in Fig. 1. From Fig. 1, the AGV dynamic model can be written as [1]: where X (t) is the longitudinal displacement, Y (t) is the lateral displacement, θ(t) represents the yaw angle, V x (t) is the longitudinal velocity, V y (t) is the lateral velocity, m ∈ R + is the mass, I z ∈ R + denotes the moment of inertia, V θ (t) is the yaw rate, F xf (t) denotes the lumped longitudinal force at the front axle, F xr (t) denotes the lumped longitudinal force at the rear axle, F yf (t) denotes the lumped lateral force at the front axle, F yr (t) denotes the lumped lateral force at the rear axle, F V θ (t) is the equivalent torque on yaw accelerationV θ (t) and F xb (t) and F yb (t) are equivalent forces of brake pedal displacement/accelerator onV x (t) andV y (t), respectively. Remark 1: Due to the symmetric property of AGV, the AGV system can be regarded as a bicycle model, i.e., the dynamic of AGV system only considers one front wheel and one rear wheel instead of two front wheels and two rear wheels. For the convention lateral AGV system in previous studies [9]- [10], the system variables only include the lateral displacement, lateral velocity, yaw angle and yaw rate. Therein, the longitudinal velocity in the resulting AGV system is regarded as a constant or known time-varying parameter. In this study, the AGV system in (1) considers longitudinal displacement, longitudinal velocity, lateral displacement, lateral velocity, yaw angle and yaw rate. Since three velocities are simultaneously considered, it is more practical for the designer to address the tracking control design problem of these velocities.
With the small angle assumption on the steering angle, two brake/accelerator forces {F xb (t), F yb (t)} can be derived as follows [2]: where α f is the tire slip angle of front wheel, C af is the stiffness coefficient w.r.t. α f , α r is the tire slip angle of rear wheel, C ar is the stiffness coefficient w.r.t. α r , δ f (t) denotes the front wheels' steering angle, δ b (t) denotes the brake/accelerator, l f is the distance between the front tire and center of gravity (CG) and l r is the distance between the rear tire and CG. Remark 2: For the Dugoff model in [3], the tire forces and brake forces on the AGV system are very complicated since it involves the combination of trigonometric functions and polynomial functions associated with δ f (t) (i.e., cos δ f (t) + δ 2 f (t)). However, under the assumption that the steering angle δ f (t) is small enough, the complicated model of these forces can be approximately modelled in (2). Moreover, it can be seen that the brake/accelerator force only influence on longitudinal velocity V x (t), i.e., F yb (t) = 0.
In general, the environmental noise and external disturbance are unavoidable in the physical AGV and these effects will deteriorate the path tracking control performance. As a result, by substituting the forces in (2) into the AGV dynamic model in (1) with the consideration of external disturbance, the AGV system in (1) can be modified as the following state space model dynamic: ∈ R 6 denotes the the external disturbance with finite energy. The system matrices in (3) are defined as follows:

B. NETWORK MECHANISM OF AGV SYSTEM
To improve the maneuverability of AGV and reduce the computational complexity, the AGV system is connected with a remote control center in the future smart city and it can be formulated as a network-based control framework in Fig. 2. Based on the transmitted information from the local AGV system, the remote control center can estimate the state of AGV system and attack signals to evaluate appropriate tracking control command to improve the tracking control performance of AGV. Since only the partial information of AGV system will be transmitted to the remote control center in the predefined sample sequence, a discrete-time observer has to be constructed to estimate the whole AGV state for the path tracking control purpose. However, in such case, the system characteristics of the local continuous-time AGV system and the discrete-time observer in control center are different and thus the observer-based tracking control design becomes a difficult problem to be handled. To address this issue, the continuous AGV dynamic model in (3) with the measurement output is discretized based on Euler-Maruyama method as follows [26]: where C(x(kh)) ∈ R m is the nonlinear measurement output, n(kh) is the measurement noise, h denotes the sample size and VOLUME 10, 2022 k ∈ N ∪ {0}. In the following, the index notation k is adopted to replace kh to simplify the notation, e.g., x(kh) is replaced by x(k). In general, due to the uncertain quality of service (QoS) in communication channel, the transmitted data (i.e., output measurement y(k) for observer and control input u(k) for AGV system) may suffer from the effect of network-induced delay and packet dropout. Hence, the actual control input u(k) received by the actuator of AGV system and sensor information y p (k) received by the remote control center are modified as follows: where u p (k) is the control input designed by the remote control center, y p (k) denotes the measurement output received by the remote control center, d RA (k) denotes the delay from remote control center to actuator, d SR (k) denotes the delay of sensor to remote control center and {α(k), β(k)} are two mutual independent random processes to formulate the effect of packet dropout. Assumption 1: Two delay sequences are bounded above and below, i.e., 0 ≤ d l, Remark 3: In (5), if the packet dropout occurs in the uplink communication (i.e., β(k) = 1), the information of current measurement output y(k) can not be transmitted to the remote control center and the remote control center will use the the information of previous measurement output y(k − 1). On the other hand, if the packet dropout does not occur in the uplink communication (i.e., β(k) = 0), the transmitted measurement output may suffer the networked-induced delay, i.e., the control center will receive the information y(k − d SR (k)).

The effect of networked induced delay and packet dropout on control input u(k) is formulated in a similar sense.
In this study, the random sequences {α(k), β(k)} are assumed to be Bernoulli sequences. Then, by the definition of Bernoulli process, the random sequences {α(k), β(k)} satisfy the following properties: where 1 >ᾱ > 0 and 1 >β > 0 are the probabilities of data dropout in the downlink communication channel and the uplink communication channel, respectively.
On the other hand, because of insecure network vulnerabilities, there may exist malicious attack signals during the transmission process and these attack signals try to deteriorate the transmitted data. In general, these attack signals may enter the the sensor and actuator via wireless channel. Hence, these undesirable effects can be regarded as equivalent actuator attack signal and sensor attack signal. With the consideration of these attack signals, the discretized AGV system and the measurement output in (4) should be modified as: where f a (k) ∈ R 2×1 is the actuator attack signal, f s (k) ∈ R s×1 represents the sensor attack signal and D(x(k)) ∈ R m×s denotes the sensor attack gain matrix. Remark 4: For the modified discretized AGV system in (6), the actuator attack signal f a (k), which came from the wireless channel in the downlink network as shown in Fig. 2, will enter the actuator to corrupt the control input u(k). Thus, to formulate this phenomenon, the ideal control input u(k) is replaced by faulty control input u(k)+f a (k) in (6). Besides, the sensor attack signal f s (k), which comes from wireless channel in the uplink network, will corrupt the sensor measurement output y(k) at the remote control center.
Remark 5: In this study, the actuator attack signal f a (k) in (6) from the wireless network will influence the perfor- (6). In other words, the actuator attack signal will deteriorate the turn around behavior of AGV system and longitudinal velocity V x (k) tracking. On the other hand, the sensor attack signal f s (k) generated by the malicious attacker from wireless channel is used to interference the estimation of measurement output. In general, different than the attack signal in system, the fault signals in system/sensor are associated to the system component units, i.e., the modeling of fault signals on system should depends on the system characteristics. However, since the attack signals are designed by the attacker, the attack signals on actuator/sensor do not limited to this and it have various type of attack signals.
In general, to estimate the attack signals in (6) for the path tracking control design by the observer at the remote side, the attack signals f a (k) and f s (k) should be modelled for the estimation. In this study, without using the conventional disturbance observer in [22] or the descriptor model in [25], the following smoothed signal model is used to describe the actuator attack signal f a (k) [27]: is the extrapolation error of future actuator attack signal f a (k + 1) and {a i ≥ 0} p i=0 is the set of extrapolation coefficients. The system matrix of the smoothed model for the actuator attack signal f a (k) is defined as: Similar to the smoothed signal model for the actuator attack signal f a (k) in (7), the smoothed signal model for the sensor attack signal f s (k) is constructed as follows: is the set of extrapolation coefficients. The system matrix of the smoothed model for the sensor attack signal f s (k) is defined as: Remark 6: For the conventional attack-tolerant control schemes on autonomous ground vehicle [22]- [25], the attack signals are modeled as an equivalent descriptor system for the estimation. In this situation, the resulting design conditions involve strict algebraic equation constraints. In general, instead of direct solving these strict algebraic equation constraints, a sub-optimal method is proposed to transform these algebraic equation constraints to specific linear matrix inequality (LMI) constraints to simplify the design. However, in the most cases, the solution (i.e., observer gains) of the specific LMI constraints is not identical to the solution of the algebraic equation constraints. Consequently, the observer gains obtained from the LMI constraints may fail in the attack-signal estimation.
Remark 7: For the smoothed signal models in (7), (8), the designer has to choose suitable extrapolation coefficients to minimize the extrapolation errors {v a (k),v s (k)} as small as possible. However, since the attack signals are unknown for the designer, it is not easy to find a fixed extrapolation coefficients for arbitrary attack signals. In this case, one possible selection of these coefficients is ( For the first property, it is expected that the future signal is more related to the current signal. On the other hand, the second property is proposed to avoid over extrapolation. Then, by augmenting the smoothed models in (7) and (8) with the discretized AGV system in (6) and delay control input in (5), the following augmented system can be constructed for the state/fault estimation: The detailed system matrices in (9) are defined as:f Remark 8: From the structure of augmented system in (9), , measurement noise n(k), extrapolation errors of actuator attack signal v a (k) and extrapolation errors of sensor attack signal v s (k). Since these external signals are unavailable for the designer, their worst-case effect on tracking performance and state/attack signal estimation of AGV system is considered in the robust H ∞ network observer-based attack-tolerant path tracking control strategy in the sequel.
Based on the augmented system in (9), the state of AGV system x(k), actuator attack signal f a (k) and sensor attack signal f s (k) can be simultaneously estimated. To achieve the observer-based tracking control design, the following Luenberger-type observer is utilized: wherex(k) is the estimated state of the augmented system in (9),ŷ(k) denotes the estimated measurement output and L(x(k)) denotes the nonlinear observer gain.
Remark 9: By using the smoothed models of actuator attack signal and sensor attack signal to construct the augmented system, the effect of these attack signals (i.e., f a (k) and f s (k)) on state variable x(k) and output measurement y(k) in (6) can be regarded as the interaction of augmented state variables in (9). As a result, instead of direct estimation of the state variable x(k) in (6) with the corruption of f a (k) and VOLUME 10, 2022 f s (k), the estimation of augmented statex(k) in (9) by the Luenberger-observer in (10) will not be corrupted by attack signals.
In general, due to the unpredictable road condition such as car accident, the pre-specified tracking trajectory should be re-specified to meet some safety requirements. Hence, by using the local information of AGV, the remote control center can specify suitable trajectory for AGV system to improve the maneuverability during the trajectory tracking process. In this study, the reference tracking trajectory is generated by the following reference model: where x r (k) ∈ R 6 is the desired trajectory to be tracked for AGV system, r(k) ∈ R 6 denotes the reference input, A r represents the system matrix with |eig(A)| < 1 and B r denotes the reference input matrix. Remark 10: In (11), the remote control center will specify the reference input r(k) to generate suitable tracking trajectory x r (k). According to design purpose, the system matrices {A r , B r } should be carefully designed since it will directly influence the transient response of x r (k). For the convenience of trajectory specification, if A r = B r are specified, then the steady state trajectory Based on the reference tracking trajectory by the reference model in (11) and the estimated statex(k) by the observer in (10), the control input calculated by the remote control center is designed as the following feedback control structure: where K (·, ·) denotes the nonlinear observer-based controller.

C. PROBLEM FORMULATION
In this study, the Luenberger-type observer in (10) is used to estimate the state of AGV system, actuator attack signal and sensor attack signal. Then, by utilizing these estimations, the nonlinear controller K (x(k), x r (k)) in (12) is implemented for the path tracking task. Since the measurement noise n(k) in sensor and the external disturbance v(k) are unavailable, these effects should be considered during the design of observer and observer-based controller. Further, for the reference model in (11), the reference input r(k) is considered as external input. Hence, the following robust H ∞ network observer-based attack-tolerant path tracking control strategy is proposed: is the tracking error, t f ∈ N is the terminal time, Q E ≥ 0 and Q T ≥ 0 are the symmetric weighting matrices associated with estimation error and tracking error, respectively, R > 0 denotes symmetric weighting matrix of control effort and V (x(0)) > 0 denotes the effect of the initial condition to be deducted. In (13), if the designer can design the nonlinear controller gain K * (x(k), x r (k)) in (12) and nonlinear observer gain L * (x(k)) in (10) such that J (L * (x(k)), K * (x(k), x r (k))) ≤ ρ, for some prescribed attenuation level ρ > 0, then the worst-case effect of reference input r(k) and external disturbancev(k) on the estimation error and tracking error can be attenuated under a prescribed attenuation level ρ from the energy perspective.

III. ROBUST H ∞ NETWORK OBSERVER-BASED ATTACK-TOLERANT PATH TRACKING CONTROL STRATEGY FOR AGV SYSTEM
In this section, the design of robust H ∞ network observerbased attack-tolerant path tracking strategy in (13) for AGV system will be addressed. To simplify the design procedure, a nonlinear augmented system to include the state of reference system, AGV system and observer sytem is needed. Further, the dimension of augmented system in (9) and reference tracking model in (11) should be unified. Thus, the reference model is extended as follows: wherex On the other hand, by subtracting the observer in (10) from the augmented system in (9), we can obtain the following By (9), (10), (14), the following augmented system of AGV can be constructed as follows: The detailed system matrices in (16) are specified as follows: To simplify the design procedure, the robust H ∞ network observer-based attack-tolerant path tracking control strategy of AGV system in (13) can be transformed to the following H ∞ stabilization control design problem of the augmented system in (16) where For the nonlinear augmented system of AGV in (16), due to the network-induced delay, there exists delayed external disturbances (i.e.,v(k − 1) andv(k − d SR (k))). For the simplicity of the design, the following assumptions are made: Assumption 2: The augmented external disturbancev(k) is zero for k = −1, −2, · · · . Assumption 3: The trajectory of augmented system in (16) lies in a compact domain , i.e.,x(k) ∈ .
Moreover, because of nonlinear system matrices in (16), it is not easy to decouple the external disturbance and system state for the design. To address this issue, the convex Lyapunov function will be adopted for the design and the corresponding definition is given as follows: Definition 1: The function V (x) is called the convex Lyapunov function if the following conditions hold: With the help of convex Lyapunov function, the design of robust H ∞ attack-tolerant observer-based tracking control of AGV system can be transformed to an equivalent nonlinear functional inequality problem in the following theorem: Theorem 1: For the augmented system of AGV in (16), if there exist a convex Lyapunov function V (x(k)), nonlinear controller gain K (x(k), x r (k))), nonlinear observer gain L(x(k)) and a set of positive constants {α < 1, β < 1, γ < 1, ρ} such that the following conditions hold: where k)), then the robust H ∞ network observer-based attack-tolerant path tracking control strategy of AGV system in (17) can be achieved with a prescribed disturbance attenuation level ρ, i.e., J (L(x(k)), K (x(k), x r (k))) < ρ. On the other hand, since the disturbancev(k) is finite energy, i.e.,v(k) will vanish as k → ∞, the augmented system in (16) is mean square stable, i.e., E{x T (k)x(k)} → 0, as k → ∞.
Proof: Please refer to Appendix A. Based on the above theorem, the robust H ∞ network observer-based attack-tolerant path tracking control strategy of AGV system is transformed to solving the nonlinear difference inequalities in (18) with the operator constraints of convex Lyapunov function V (x(k)) in (19).

IV. FUZZY ROBUST H ∞ NETWORK OBSERVER-BASED ATTACK-TOLERANT PATH TRACKING CONTROL STRATEGY FOR AGV SYSTEM
In this study, Takagi-Sugeno (T-S) fuzzy interpolation method is utilized to approximate the nonlinear AGV system by the interpolation of a set of local linearized AGV systems in (21). In fact, due to the nonlinearitiy of autonomous ground vehicle (AGV) system, the design condition for robust H ∞ network observer-based attack-tolerant path tracking control strategy in (13) is transformed to equivalent nonlinear difference inequalities in (18)- (19). Generally speaking, these nonlinear difference inequalities can not be solved analytically or numerically. As a result, with the merit of T-S fuzzy interpolation method, the design condition of the robust H ∞ network observer-based attack-tolerant path tracking control strategy in (13) can be derived in terms of a set of LMIs constraint problem, which can be solved efficiently via current convex optimization method.
To begin with, the ith plant rule for the discretized AGV system in (6) is given as [32] The ith Plant Rule : where {z i (k)} o i=1 denotes the set of premise variables, o is the total number of premise variables, j,i denotes the membership function of the jth premise variables w.r.t. the ith rule and g is the total number of plant rules. Then, by the defuzzification process, the nonlinear AGV system in (6) can be represented as [32] x(k is the normalized grade membership function w.r.t. the jth premise variable of the ith plant rule and h i (z(k)) is the interpolation function associated with the ith rule. The physical meaning of (21) is to interpolate g local linearized systems through g fuzzy interpolation functions {h i (z(k))} g i=1 to approach nonlinear AGV system in (6).
Remark 11: In general, based on the nonliearity of AGV system in (6), the premise variables can be chosen as the yaw angle θ(k), the longitudinal velocity V x (k), the lateral velocity V y (k) and the yaw rate V θ (k). Then, to construct the local linearized systems, the operation points of these premise variables can be chosen according to the desired trajectory of maneuvering task of AGV system. For example, if the longitudinal velocity V x (k) is asked to motion within 10m/s~20m/s, the corresponding operation points can be chosen as V x,1 = 10 and V x,2 = 20 for the premise variable V x (k).
To ensure the completeness of fuzzy AGV system in (21), the following assumption is made [32] Assumption 4: The interpolation functions {h i (z(k))} g i=1 satisfy the following two properties (i) h i (z(k)) ≥ 0, ∀i = 1, · · · , g, and (ii) g i=1 h i (z(k)) = 1. By the fuzzy-based AGV system in (21), the dynamic system of augmented statex (9) can be rewritten as: Before the further discussion, the following theorem is provided to address the observability of the ith local fuzzy augmented system in (22) Theorem 2: The ith local fuzzy augmented system in (22) is observable, if the ith local fuzzy system in (21) is observable, i.e., and the following conditions hold where Z denotes complex domain of z. Proof: Please refer to Appendix B. Remark 12: By using the conventional rank test [28] (i.e., Theorem 2) and with adequate choice of A a and A s (i.e., the extrapolation coefficients {a i , b i } p i=0 ), the observability of local augmented system can be guaranteed. Based on parallel distribution compensation, one linear observer is applied for each local augmented system and the fuzzy Luenberger-type observer in (29) (22) is a nonlinear system. In this case, to ensure the observability of augmented system in (22), the designer have to examine complicated state-dependent rank condition [33].

can be constructed by the interpolation of local linear observers. However, even the augmented system is the interpolation of several local linear systems, the augmented system in
In the above theorem, the extrapolation coefficients {a i } p i=0 in (7) and {b i } p i=0 in (8) should satisfy with (24)- (27) to guarantee the observability of the fuzzy augmented AGV system in (22). Then, to simultaneously estimate the state/attack signals in (22), the following jth observer rule is given: The jth Observer Rule : where y p (k) = (1 − β(k))y(k − d SR (k)) + β(k)y(k − 1) and L j denotes the jth observer gain. Then, by the defuzzification process, the fuzzy Luenberger observer can be inferred as follows: Moreover, by the estimated state in (29), the lth controller rule can be constructed as

The lth Controller Rule :
If where {K 1,l , K 2,l } is the fuzzy controller gains of the lth control rule. Similar to the fuzzy Luenberger-type observer in (29), the fuzzy path tracking controller can be implemented as By subtracting the fuzzy observer in (29) from the the augmeneted system in (22), the estimation error system e(k) can be obtained as follows e(k + 1) Then, by letting the augmented state asx(k) = [x T r (k),x T (k), e T (k)] T , the corresponding closed-loop dynamic system can be obtained as follows Before the further discussion, the following Lemmas are given to facilitate the design Lemma 1: (see [29]) Given a set of matrices {T i } N i=1 , a positive definite matrix P and a positive series {α i ≥ 0} N i=1 , which satisfies N i=1 α i = 1, the following inequality holds: α i T T i PT i Lemma 2: (see [30]) Given two matrices A, B and a positive definite matrix P, the following inequality holds: Based on above Lemmas, we can get the following result Theorem 3: If there exist fuzzy controller gains (29) and positive definite matrices ,j,f ,l,s=1 , W 1 , P 2 , P 3 , P 4 , P 5 , P 6 , such that the following LMIs hold and the following matrices (17) can be achieved with a prescribed disturbance attenuation level ρ, i.e., J (L(x(k)), K (x(k), x r (k))) < ρ. On the other hand, since the disturbancev(k) is finite energy, i.e.,v(k) will vanish as k → ∞, the augmented system in (33) is mean square stable, i.e., E{x T (k)x(k)} → 0, as k → ∞.

then the robust H ∞ network observer-based attack-tolerant path tracking control strategy in
Proof: Please refer to Appendix C. In Theorem 3, the robust H ∞ network observer-based attack-tolerant path tracking control strategy design for nonlinear AGV system in (6) is transformed to an equivalent LMIs constrained problem in (34)-(35), which can be easily solved via MATLAB LMI TOOLBOX. Moreover, to achieve the optimal attenuation level ρ * in (34)-(35), the following optimal robust H ∞ attack-tolerant observer-based path tracking control strategy of AGV is formulated as follows is the set of design variables.
Based on above design analysis, the design procedure of the robust H ∞ network observer-based attack-tolerant path tracking control strategy design for the nonlinear AGV system is given as follows STEP I Choose the extrapolation coefficients {a i , b i } i=0 for the construction of smoothed actuator/sensor attack signal models in (7) and (8) and specify the matrices {A r , B r } and reference input r(k) to construct the reference model in (11).
STEP II Choose suitable fuzzy premise variables with the corresponding operation points to construct the T-S fuzzy AGV system in (20) and then construct the augmented system ofx(k) in (33).
STEP III Choose the weighting matrices {Q E ≥ 0, Q T ≥ 0, R > 0} of the robust H ∞ network observer-based attack-tolerant path tracking control strategy in (13) according to the design purpose. Then, solve the optimal robust H ∞ network observer-based attack-tolerant path tracking control problem in (36) to obtain the optimal attenuation level ρ * , fuzzy controller gains {K * 1,j , K * 2,j } g j=1 and fuzzy observer gains

V. SIMULATION EXAMPLE
For the application of AGV in future smart city, the AGV system is asked to track a reference trajectory through CAN via wireless network in city environment to achieve some specific tasks. However, due to the insecure networked system and the wireless induced effect, the path tracking and state estimation for single AGV in city environment become more difficult. For example, the state estimation in the networked-control system of city environment will be severely deteriorated by the wireless interference and malicious attack signals [31].
To address this issue, the effects caused by insecure network and wireless channel will be formulated as equivalent actuator/sensor attack signals in this simulation.

A. STRUCTURE OF PHYSICAL AGV SYSTEM AND CYBER NETWORK SYSTEM
By the bicycle model in [2], the detailed parameters of AGV system are given as: m = 1280(kg), I z = 2500(kg/m 2 ), C af = C ar = 3×10 4 (N /rad), l f = 1.2(m) and l r = 1.22(m). Also, for the measurement output in (6) To construct the network structure in Fig. 2, the sampling period h is set as 10 −3 (sec); the upper/lower bounds of networked-induced delay are given as d l,RA = 0, d u,RA = 3h, d l,SR = 0 and d u,SR = 3h; the means of two Bernoulli sequences α(k) and β(k) are given asᾱ = 0.001 and β = 0.001, respectively. Furthermore, for the attack signal estimation, the extrapolation parameters of the 2nd order actuator/sensor smoothed signal models in (7) and (8) are given as: a 0 = 0.9, b 0 = 0.7, a 1 = 0.06, b 1 = 0.2, a 2 = 0.04, b 2 = 0.1 to satisfy with the observability of T-S fuzzy based AGV system in (22). Due to the insecure CAN, the actuator/sensor attack signals are set as For the first actuator attack signal f a,1 (k), it aims to generate constant disturbance to influence the steering angle of front wheel δ f (t) and thus the AGV system will deviate from the reference trajectory. On the other hand, the second actuator attack signal f a,2 (k) influences the brake pedal/accelerator δ b (t) and it will cause undesired acceleration or deceleration. Moreover, due to the uncertain wireless communication channel, the transmitted signal y(k) is deteriorated by the single frequency sensor attack signal f s (k).

B. FUZZY MODEL CONSTRUCTION AND OBSERVER-BASED CONTROLLER DESIGN
Based on T-S fuzzy approach in [32], four premise variables , ω z (k)} are selected with the following operation points Then, by choosing trapezoidal membership functions, the nonlinear AGV system in (3) can be formulated as the following fuzzy-model-based AGV system: is the set of local system matrices. Moreover, the weighting matrices {Q E ≥ 0, Q T ≥ 0, R > 0} in the robust H ∞ network observer-based attacktolerant path tracking control strategy of AGV system in (13) are chosen as For the selection of weighting matrices in (40), the designer considers that the position/angle tracking is more important than the velocity tracking. In this case, the weighting coefficients associated with position/angle tracking in Q T are bigger than the weighting coefficients associated with velocity tracking. On the other hand, since the state estimation and attack signal estimation are equivalently important, the weighting coefficients for all variable estimations are identical in Q E .
Then, by solving the optimal robust H ∞ network observerbased attack-tolerant path tracking control strategy of AGV in (36) with the optimal disturbance attenuation level ρ * = 1.5, the fuzzy controller gains {K * 1,j , K * 2,j } 24 j=1 and fuzzy observer gains {L * i } 24 i=1 can be obtained for the construction of fuzzy controller in (31) and fuzzy observer in (29), respectively.

C. SIMULATION RESULTS
In this section, to illustrate the merit of proposed method, the fuzzy robust observer-based steering control scheme of AGV in [9] is implemented for the tracking performance comparison. Since the longitudinal distance and longitudinal velocity are not considered in [9], their values are set as same as the reference signal in the simulation. Thus, the corresponding tracking/estimation results are omitted. In this simulation, the AGV system is asked to perform a double lane change task during the whole manuevering process as shown in Fig. 3, i.e., two turn around maneuverings.
The controlled six AGV states with the reference trajectory and 2-D trajectory of AGV system by the proposed method and the method in [9] are shown in Figs. 3-6. By the proposed method, due to the efficient estimation of attack signals in Fig. 9 and AGV states in Figs. 10-12, the controlled longitudinal velocity V X (k), lateral velocity V Y (k) and yaw rate V θ (k) can track the desired reference velocities with very slight fluctuation. For example, once the magnitude of f a,1 (k) is changed and estimated at 25s in Fig. 9, the control input will utilize the estimatedf a,1 (k) to change it's magnitude for attack 58344 VOLUME 10, 2022  signal compensation on the control of lateral velocity V Y (k) and yaw rate V θ (k) in Fig. 7. Thus, from Figs. 5-6, the controlled lateral velocity V Y (k) and yaw rate V θ (k) do not have any deviation, i.e., the effect of f a,1 (k) on V Y (k) and V θ (k) is efficiently attenuated. From the 2-D trajectory of AGV system in Fig. 3, the controlled AGV system can achieve the maneuvering task with the maximum offset 0.8m. For the fuzzy robust observer-based controller in [9], the controlled AGV system states are oscillating due to the fluctuation of the estimated states in Figs. 10-12. Therein, caused by the fluctuation of the estimated yaw rateV θ (k) in Fig. 11, the controlled lateral distance Y (k) in Fig. 5 can not be maintained at the desired trajectory and it makes the AGV system circle around the desired trajectory in Fig. 3 with the maximum offset 4.8m. The two Bernoulli sequences about the downlink data dropout and uplink data dropout with two delay sequences are shown in Fig. 8. Due to these network-induced effects, the remote observer receives the delay measurement output of AGV system and it causes some jump phenomena in the observer-based feedback control signal synthesis in Fig. 7. Also, once the attack signal f a (k) is estimated, the control input uses the estimated attack signalf a (k) for attack signal elimination in Fig. 7. Once the attack signal f a (k) is estimated, the control input uses the estimated attack signalf a (k) for attack signal elimination. On the other hand, due to the networked induced delay, the control input has some rapid jump phenomena. The attack signal estimations by the proposed method are shown in Fig. 9. From Fig. 9, since the feedback information for fuzzy observer is y p (k) −ŷ(k) in (29) for the estimations of state/attack signal, the attack signal estimations {f a (k) = [f a,1 (k),f a,2 (k)] T ,f s (k)} will be influenced by the estimation of AGV state for the proposed robust H ∞ network observer-based attack-tolerant path tracking control strategy. For example, for the small estimation error in the lateral velocity V Y (k) at 35s in Fig. 11, there exists a fluctuation in the estimation of first actuator attack signal f a,1 (k) at 35s. However, once the lateral velocity V Y (k) is estimated, the estimation of first actuator attack signalf a,1 (k) approaches to the real first actuator attack signal f a,1 (k). On the other hand, even the second actuator attack signal f a,2 (k) is almost estimated for attack signal compensation, it still causes some small fluctuation on the tracking of longitudinal velocity. In this case, the phenomenon makes a slightly delay between the estimation of sensor attack signalf s (k) and real sensor attack signal f s (k). Despite these minor estimation errors of attack signals during the estimation process, these estimated attack signals can be efficiently used for the attack signal compensation during the tracking control process.   The estimation of six AGV states by the proposed method and [9] are shown in Figs. 10-12 for comparison. For the proposed estimation scheme with the compensation of actuator attack signal and sensor attack signal, the longitudinal displacement X (k), lateral displacement Y (k) and yaw angle θ(k) with the corresponding three velocities can be efficiently estimated with relatively small oscillation caused by the random external disturbance v(k), random measurement noise n(k) and minor estimation error of sensor attack signal. For example, in the estimation of longitudinal displacement X (k) in Fig. 10, the sensor attack signal on the sensor of longitudinal displacement X (k) is 2.1 sin t and it's effect may be magnified by the observer gain to observer system. Also, the actuator attack signal f a,2 (k) may cause random acceleration in V X (k). However, by using the estimated sensor attack signalf s (k) and estimated actuator attack signalf a,2 (k), the resulting estimation error can be efficiently attenuated with the maximum magnitude 1m and average estimation error 0.3m. Besides, for the robust fuzzy observer in [9], the sensor attack signal is regarded as measurement noise during the design. However, since the effect of sensor attack signal on the observer by [9] can not be passively attenuated during the estimation process, it can be seen that the estimation of AGV states is with some oscillation due to the trigonometric sensor attack signal f s (k). Further, once the turn around command is generated in control input at 3s, 8s, 33s and 38s, the robust fuzzy observer in [9] will be influenced and thus the estimation error of lateral velocity V Y (k) and yaw rat V θ (k) will increase.

VI. CONCLUSION
In this study, a robust H ∞ network observer-based attacktolerant path tracking control design is proposed for the AGV under the effect of external disturbance, measurement noise and actuator/sensor attack signals. A more practical AGV dynamic model is applied to describe the interaction among the longitudinal velocity, lateral velocity and yaw rate. Based on the concept of CAN, a networked-based AGV control system is constructed with the consideration of actuator/sensor attack signal and network-induced effects. By using two novel smoothed signal models to describe these attack signals, these attack signals can be simultaneously estimated with AGV system state by the conventional Luenbergertype observer. Then, a robust H ∞ network observer-based attack-tolerant path tracking controller is constructed to attenuate the effect of unknown disturbance on the path tracking error and eliminate the influence of attacks signals from the energy perspective. The design conditions of robust H ∞ observer-based path tracking controller are derived in terms of a set of nonlinear difference inequalities. Instead of solving a set of nonlinear difference inequalities, T-S fuzzy system is applied to approximate the nonlinear AGV system and the robust H ∞ network observer-based attack-tolerant path tracking control strategy design problem can be simplified to solving a set of LMIs. From the simulation result, the AGV can achieve a better double lane change steering task by the proposed fuzzy H ∞ observer-based attack-tolerant scheme under CAN with the networked-induced delay and packet dropout than the conventional fuzzy H ∞ observerbased control scheme. Further, the actuator/sensor attack signals in CAN could be efficiently estimated and eliminated by the observer-based feedback compensation to improve the path tracking performance. In future, to achieve some more difficult steering tasks, multi-AGVs in CAN will be controlled to maneuver in the desired path with a team formation shape. As a result, the networked-based team formation tracking problem for large-scale AGVs will be our future research topic. On the other hand, to achieve with more accuracy for attack signal modeling, the time-invariant extrapolation coefficients of smoothed models in (7), (8) should be updated to ensure the optimal extrapolation performance. Thus, the attack signal estimation with time-varying extrapolation parameters will be another future research topic.

APPENDIX A: PROOF OF THEOREM 1
Choose a convex Lynapunov functional V (x(k)), then the numerator in the robust H ∞ network observer-based attacktolerant path tracking control performance in (17) can be written as: By substituting the dynamic of augmented system in (16) into (41), we have: To decouple the disturbance terms and state dependent terms in convex Lyapunov functional V (·), the convex property is utilized and we immediately have: where α ∈ (0, 1). By the similar derivation in (43), we have the following result where γ , β ∈ (0, 1). By substituting (43)-(44), (42) can be relaxed as follows: In (45), even the state-dependent terms are decoupled with other disturbance terms, these disturbance terms are still implicit in the Lynapunov function and are coupled with time-varying matrices {D 1 ,D 2 (x(k), k),D 3 (x(k), k)}. By the assumption 2, there exist a set of scalars {τ i > 0} 3 i=1 such that the following conditions hold Also, the following conditions associated with the Lyapunov function are made: Then, with the help of (46) and (47), the disturbance terms can be relaxed as follows: By using the relations in (48)-(50), (45) can be relaxed as: Clearly, if the following nonlinear matrix inequality in (18) holds, then (51) can be written as: Also, by Assumption 1, the summation of delayed external disturbances is bounded above by the summation of delay-free external disturbance: By the facts in (53), (54), we immediately have the following result: which shows the robust H ∞ network observer-based attacktolerant path tracking control strategy in (17) can be achieved with a prescribed disturbance attenuation level ρ. Besides, since the augmented noisev(k) is of finite energy, i.e., E{ ∞ k=0v T (k)v(k)} < ∞, the right hand side of Eq. (55) is finite for t f → ∞, i.e., Due to the fact that E{V (x(0)} and ρ{ ∞ k=0v T (k)v(k)} is finite, the above inequality immediately implies the augmented system in (16) is mean square stable in probability.

APPENDIX B: PROOF OF THEOREM 2
By the rank test of observability in [28], the ith local fuzzy augmented system in (22) is observable if the following rank condition holds To show the rank condition in (56), the proof can be separated as two cases with (i) z ∈ Z\eig(hA i +I )∪eig(A a )∪ eig(A s ) and (ii) z ∈ eig(hA i + I ) ∪ eig(A a ) ∪ eig(A s ).
In the case (i), for z ∈ Z\eig(hA i + I ) ∪ eig(A a ) ∪ eig(A s ), the following rank conditions hold: In the case (ii), by using the eigenvalue condition in (24) and the rank condition in (25), the rank condition in (56) can be decoupled as follows Then, by using the rank conditions in (23), (26) and (27) which shows the fact that the rank condition in (56) is satisfied in case (ii). The proof is done.

APPENDIX C: PROOF OF THEOREM 3
The derivation of this theorem is separated two parts. In the first part, the sufficient condition for the design of robust H ∞ network observer-based attack-tolerant path tracking control strategy in (13) is derived. Then, in the second part, some matrix inequality methods are applied to transform the derived sufficient conditions into solvable LMIs.

Part (I):
To begin with, the following Lyapunov functional is selected where P i > 0 is positive definite matrix to be designed, for i = 1, · · · , 6. Then, by taking the difference of Lyapunov where W 1 = P −1 1 . By substituting (71) into the right hand side of (69) with (72), (69) can be relaxed as  He has been a Lecturer, an Associate Professor, and a Professor at the Tatung Institute of Technology, from 1973 to 1987. He is currently the Tsing Hua Distinguished Chair Professor of electrical engineering and computer science at the National Tsing Hua University, Hsinchu, Taiwan. His current research interests include control engineering, signal processing, and systems biology. He has received the Distinguished Research Award from the National Science Council of Taiwan four times. He is a National Chair Professor of the Ministry of Education of Taiwan. VOLUME 10, 2022