Integrated event-triggered fault estimation and fault-tolerant control for discrete-time fuzzy systems with input quantization and incomplete measurements

This paper addresses the problem of robust integrated fault estimation (FE) and fault-tolerant control (FTC) for a class of discrete-time networked Takagi–Sugeno (T–S) fuzzy systems with two-channel event-triggered schemes, input quantization and incomplete measurements. The incomplete information under consideration includes randomly occurring sensor saturation and randomly occurring quantization. In order to save the limited networked resources, this paper firstly proposed a novel dynamic event-triggered scheme on the sensor side and a static one on the controller side. Secondly, an event-triggered FE observer for the T–S fuzzy model is designed to estimate actuator faults and system states, simultaneously. Then, a specified discrete sliding surface in the state-estimation space is constructed. By using time-delay analysis technique and considering the effects of event-triggered scheme, quantization, networked conditions, actuator fault and external disturbance, the sliding mode dynamics and error dynamics are unified into a new networked time-delay model. Based on this model, sufficient conditions are established such that the resulting augmented fuzzy system is stochastically stable with a prescribed H_∞ performance level with a single-step linear matrix inequality (LMI) formulation. Furthermore, an observer-based sliding mode controller for reaching motion is synthesized to guarantee the reachability of the sliding surface. Finally, a single-link flexible manipulator example is present to illustrate the effectiveness of the proposed method.     

Event-triggered fault estimation and sliding mode fault-tolerant control for a class of nonlinear networked control systems

This paper is concerned with integrated event-triggered fault estimation (FE) and sliding mode fault-tolerant control (FTC) for a class of discrete-time Lipschtiz nonlinear networked control systems (NCSs) subject to actuator fault and disturbance. First, an event-triggered fault/state observer is designed to estimate the system state and actuator fault simultaneously. And then, a discrete-time sliding surface is constructed in state-estimation space. By the use of a reformulated Lipschitz property and delay system analysis method, the sliding mode dynamics and state/fault error dynamics are converted into a unified linear parameter varying (LPV) networked system model by taking into account the event-triggered scheme, actuator fault, external disturbance and network-induced delay. Based on this model and with the aid of Lyapunov–Krasovskii functional method, a delay-dependent sufficient condition is derived to guarantee the stability of the resulting closed-loop system with prescribed H_∞ performance. Furthermore, an observed-based sliding mode FTC law is synthesized to make sure the reachability of the sliding surface. Finally, simulation results are conducted to verify the effectiveness of the proposed method.     

Asynchronous sliding mode control of semi-Markovian jump systems with state saturation

This paper deals with the sliding mode control problem for semi-Markovian jump systems with state saturation, in which the controller may not be synchronized with the considered systems. A mode-detector is introduced to estimate the unavailable system mode, based on which an asynchronous sliding mode controller is designed. Then, both the $\mu$-exponential mean-square stability and the reachability of sliding surface are analyzed. Furthermore, a solving algorithm is given to acquire the feasible controller gains. Finally, the proposed asynchronous sliding mode control approach under state-saturation is illustrated via simulation results.     

Discrete control of nonlinear stochastic systems driven by Lévy process

In this paper, the stabilization is studied for a complex dynamic model which involves nonlinearities, uncertainty, and Lévy noises. This paper also discusses the controller discretization and presents a new algorithm to obtain the upper bound for the sample interval through which the exponential stability of the discrete system can still be guaranteed. Firstly, an integral sliding surface is designed to obtain the sliding mode dynamics for the considered stochastic Lévy process. By using Lyapunov theory, generalized Itô formula and some inequality techniques, the exponential stability is proved in the sense of mean square for sliding mode dynamics. The reachability of the sliding mode surface is also ensured by designing a sliding mode control law. Secondly, the continuous-time controller is discretized from the point of control cost, and the squared difference is analyzed for the states before and after the discretization. Different from those classical stochastic differential equations driven by Brownian motions, the noise is supposed to be Lévy type and the squared difference is analyzed in different cases. Furthermore, we obtain the largest sampling interval through which the discretized controller can still stabilize the Lévy process driven stochastic system. Finally, a simulation for a drill bit system is given to demonstrate the results under the algorithms.     

Barrier function-based nonsingular prescribed performance terminal sliding mode tracker for under-actuated nonlinear systems: Experimental study

In this paper, an adaptive concave barrier function scheme coupled with the non-singular terminal sliding mode control technique is proposed for finite-time tracking control of the under-actuated nonlinear system in the existence of model uncertainty, external disturbance and input saturation. Firstly, the dynamical equation of under-actuated nonlinear n-order system is expressed under model uncertainty, external disturbance and input saturation. Secondly, for the improvement of stability performance of the system in the existence of input saturation, a compensation system is designed to overcome the constraint on the control input. Afterward, the tracking errors between actual states of the system and differentiable reference signals are defined and the sliding surface based on the defined tracking errors is presented. Then, for gaining the better transient and steady-state performance of the closed-loop system, the prescribed performance control scheme is adopted. Based on this method, the transformed prescribed form of the previous determined sliding surface is obtained to ensure that the sliding surface can reach to a predefined region. Afterward, for assurance of the finite-time reachability of transformed sliding surface, the nonsingular terminal sliding surface is recommended. In addition, for the compensation of the model uncertainty and external disturbance existed in the system, the adaptive-based concave barrier function technique is used to estimate the unknown bounds of uncertainty and exterior disturbance. Finally, for demonstration of the proposed control method, the simulations and experimental implementation are done on the air levitation system.     

Sliding mode output-feedback control of discrete-time Markov jump systems using singular system method

The issue of adaptive sliding mode controller design via output knowledge is studied for discrete-time Markov jump systems in this paper by means of using singular system scheme. To force the system state onto the sliding motion, an appropriate switching surface depended on the system output is established. Meanwhile, the reachability of the sliding manifold is guaranteed by synthesizing the robust sliding mode controller and adaptive sliding mode controller for the accessible and inaccessible upper bounds of sliding patch, respectively. By using Lyapunov functional technique, sufficient criteria to guarantee the sliding motion to be stochastically admissible are proposed. Then the reachability conditions of the predesigned switching surface are developed. Finally, simulation results are provided to illustrate the effectiveness of the proposed approach.     

Nested backward compensation of unmatched perturbations via HOSM observation

This paper tackles the compensation problem of linear time invariant systems affected by unmatched perturbations. The proposed methodology exploits a high order sliding mode observer, guaranteeing theoretically exact state and perturbation estimation. A compensation based strategy is proposed to cope with the unmatched perturbations. The compensation of the desired coordinate is carried through a nested backward sliding surface design, which compensates some of the non-actuated state components, while the remaining states are maintained to be bounded. The feasibility of the technique was tested in an active suspension vehicle system.¹     

Event-triggered sliding mode control of uncertain switched systems under denial-of-service attacks

This study is concerned with the event-triggered sliding mode control problem for a class of cyber-physical switched systems, in which the Denial-of-Service (DoS) attacks may randomly occur according to the Bernoulli distribution. A key issue is how to design the output feedback sliding mode control (SMC) law for guaranteeing the dynamical performance of the closed-loop system under DoS attacks. To this end, an event-triggered mechanism is firstly introduced to reduce the communication load, under which the measurement signal is transmitted only when a certain triggering condition is satisfied. An usable output signal for the controller is constructed to compensate the effect of unmeasured states and DoS attacks. And then, a dynamic output feedback sliding mode controller is designed by means of the attack probability and the compensated output signals. Both the reachability and the mean-square exponential stability of sliding mode dynamics are investigated and the corresponding sufficient conditions are obtained. Finally, some numerical simulation results are provided.     

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T²)$O\left(T^2\right)$ where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF).     

Asynchronous output feedback control for fuzzy Markovian jump systems via sliding mode

This paper investigates the design problem of asynchronous output feedback controller via sliding mode for a class of discrete-time fuzzy Markovian jump systems. Considering the non-synchronization phenomenon between the Markovian jump systems and the sliding controller, an asynchronous control method with a stochastic variable is adopted to describe the connections of the systems and controller. On the other hand, not full of states are accessible for the controller since it is impossible or very expensive to estimate all of states, while the output information can be acquired to the controller all the time. Based on the above aspects, the asynchronous output feedback controller via sliding mode for fuzzy Markovian jump systems is investigated to ensure the sliding mode dynamics to be stochastically stable, besides, several sufficient conditions are given to find a set of feasible solutions of the controller parameters. The asynchronous sliding mode control law is synthesized to guarantee the reachability of the trajectories of the closed-loop systems. Finally, a simulation example is to verify the effectiveness of the control strategy.     

Finite-time sliding mode flow control design via reduced model for a connection-oriented communication network

This paper addresses the flow control design of a connection-oriented communication network from the robust control theory perspective. Network is modelled as a nth order discrete system whose first order model is obtained using the two-time scale property associated with the process. The proposed scheme is characterised by an equivalent control based discrete sliding mode design for the first order model which is applied to nth order systems through aggregation. Besides its design simplicity, the proposed method exhibits finite time convergence property for the states while applied to the full order system emulating the characteristics of terminal sliding mode in a certain way. Simulation results via Matlab and ns-2 validate the efficacy of the proposed algorithm as an effective flow controller for connection-oriented networks.     

Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems

In this paper, the observer-based sliding mode control (SMC) problem is investigated for a class of uncertain nonlinear neutral delay systems. A new robust stability condition is proposed first for the sliding mode dynamics, then a sliding mode observer is designed, based on which an observer-based controller is synthesized by using the SMC theory combined with the reaching law technique. Then, a sufficient condition of the asymptotic stability is proposed in terms of linear matrix inequality (LMI) for the overall closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability problem is also discussed. It is shown that the proposed SMC scheme guarantees the reachability of the sliding surfaces defined in both the state estimate space and the state estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility of the proposed design scheme.     

Triggered-based exponential sliding mode tracking strategy for DCPSs with disturbance

In this paper, the problem of tracking control for discrete cyber physical systems (DCPSs) with disturbance is studied, and the exponential sliding mode tracking strategies via event-triggered are presented. Firstly, for the purpose of reducing chattering in sliding-mode, a new exponential-type reaching law is designed, furthermore, the reachability of sliding surface is verified. Then, the sliding mode tracking schemes under event-triggered are presented, among which two event-triggered strategies are proposed to save network resources. Furthermore, the reachability of designed methods and the boundness of tracking errors are proved. Finally, the feasibility of the presented methods is proved by two simulation examples.     

Stabilization and destabilization of nonlinear systems via intermittent stochastic noise with application to memristor-based system

This paper considers the stabilization and destabilization of a given nonlinear system by an intermittent Brownian noise perturbation. We give some distinct conditions and conclusions on almost sure exponential stability and instability, which are related to the control period T and the noise width δ. These results are then exploited to examine stabilization and destabilization via intermittent stochastic perturbation and applied to the stabilization of a memristor-based chaotic system. Two numerical examples are presented to illustrate the theoretical results.     

Fractional-order adaptive neuro-fuzzy sliding mode H∞ control for fuzzy singularly perturbed systems

This paper investigates the fractional-order (FO) adaptive neuro-fuzzy sliding mode control issue for a class of fuzzy singularly perturbed systems subject to the matched uncertainties and external disturbances. Firstly, a novel FO fuzzy sliding mode surface is presented. Secondly, by introducing an appropriate ε-dependent Lyapunov function, some H_∞ performance analysis criteria are given, which also ensure the robust stability of the sliding mode dynamics. Furthermore, a hybrid neuro-fuzzy network system (HNFNS) is introduced to estimate the matched uncertainty. Moreover, an FO adaptive fuzzy sliding mode controller is designed to drive the state trajectories of fuzzy singularly perturbed systems to the predefined FO sliding mode surface within a finite-time. Finally, two verification examples are presented to illustrate the validity of the proposed FO control scheme.     

Event-triggered sliding mode control for networked linear systems

This paper investigates the control-based event-triggered sliding mode control for a networked linear system whose feedback information is transmitted over a digital communication network. In this paper, a novel event-triggered mechanism based on control value is proposed. Different from traditional event-triggered mechanisms that are normally based on states, our mechanism pays more attention to the desired control input value of the system. When the deviation between the current control input and the control input being calculated on the basis of the previous system state exceeds a given threshold, an event is triggered. For the sake of reducing the information to be transmitted, a quantization policy is executed and only a few bits are needed to transmit the feedback symbol of each sample. The combination of the control-based event-triggered mechanism and the quantization policy can significantly reduce both the transmission frequency and the number of bits of each feedback packet. For the concerned system, sliding mode control is implemented. The reachability of the sliding mode surface and the robust stability of the system are analyzed by fully taking quantization effects into account. Moreover, the effects of transmission delay of feedback packets on the event-triggering mechanism are considered. Under the proposed mechanism, the lower bound of event intervals is proven to be non-zero, i.e., the Zeno behavior is excluded. Simulations of a mechanical system are done to further verify the superiority of the proposed mechanism.     

Observer-based sliding mode control for a class of discrete systems via delta operator approach

In this paper, an observer-based sliding mode control (SMC) problem is investigated for a class of uncertain delta operator systems with nonlinear exogenous disturbance. A novel robust stability condition is obtained for a sliding mode dynamics by using Lyapunov theory in delta domain. Based on a designed sliding mode observer, a sliding mode controller is synthesized by employing SMC theory combined with reaching law technique. The robust asymptotical stability problem is also discussed for the closed-loop system composed of the observer dynamics and the state estimation error dynamics. Furthermore, the reachability of sliding surfaces is also investigated in state-estimate space and estimation error space, respectively. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the developed method.     

Fault-tolerant control for the linearized spacecraft attitude control system with Markovian switching

In this article, the fault-tolerant control is investigated for the spacecraft attitude control system described by a linearized model with Markovian switching. First, the evolution of sudden failures of the spacecraft’s actuators is described by a Markov process. Then, the mathematical model of the spacecraft attitude control system with the Markov jump characteristic fault is established. Taking the uncertainty of the system model and external interference into consideration, a fault-tolerant control scheme is proposed for the established spacecraft attitude control system with the Markov jump characteristic fault by using the sliding mode control technique. Compared with some existing sliding mode controller design methods, the proposed method requires a less total number of LMIs to be solved. The stability and reachability of the resulting closed-loop system under the presented sliding mode control scheme are proven by applying the Lyapunov stability theory. Finally, some simulation results are provided to show the effectiveness and advantages of the proposed control method for spacecraft attitude control.