Robust reliable L2 – L∞ control for continuous‐time systems with nonlinear actuator failures

This article examines the reliable L₂ – L_∞ control design problem for a class of continuous‐time linear systems subject to external disturbances and mixed actuator failures via input delay approach. Also, due to the occurrence of nonlinear circumstances in the control input, a more generalized and practical actuator fault model containing both linear and nonlinear terms is constructed to the addressed control system. Our attention is focused on the design of the robust state feedback reliable sampled‐data controller that guarantees the robust asymptotic stability of the resulting closed‐loop system with an L₂ – L_∞ prescribed performance level γ > 0, for all the possible actuator failure cases. For this purpose, by constructing an appropriate Lyapunov–Krasovskii functional (LKF) and utilizing few integral inequality techniques, some novel sufficient stabilization conditions in terms of linear matrix inequalities (LMIs) are established for the considered system. Moreover, the established stabilizability conditions pave the way for designing the robust reliable sampled‐data controller as the solution to a set of LMIs. Finally, as an example, a wheeled mobile robot trailer model is considered to illustrate the effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 309–319, 2016     

Event-triggered control for sampled-data set stabilization of switched delayed boolean control networks

This paper considers the event-triggered control design for the uniform sampled-data set stabilization of switched delayed Boolean control networks (SDBCNs). First, using the algebraic state space representation method, SDBCNs are converted into the equivalent algebraic form. Second, using the algebraic form, the uniform sampled-data reachable sets are constructed, based on which, a necessary and sufficient condition is obtained for the uniform sampled-data set stabilization of SDBCNs. Finally, the event-triggered mechanism is presented, and a sufficient condition is proposed to design the time-variant state feedback event-triggered controller for the uniform sampled-data set stabilization of SDBCNs.     

Reliable control for nonlinear systems with stochastic actuators fault and random delays through a T-S fuzzy model approach

This paper considers the reliable control design for T-S fuzzy systems with probabilistic actuators faults and random time-varying delays. The faults of each actuator occurs randomly and its failure rates are governed by a set of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of each actuator and time-varying random delays, new fault model is proposed. Based on the new fuzzy model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of T-S fuzzy systems are derived by using Lyapunov functional method and linear matrix inequality (LMI) technique. It should be noted that the obtained criteria depend on not only the size of the delay, but also the probability distribution of it. Finally, a numerical example is given to show the effectiveness of the proposed method.     

Robust reliable control for uncertain switched nonlinear systems with time delay under asynchronous switching

This paper investigates the problem of robust reliable control for a class of switched nonlinear systems with time delay and actuator failures under asynchronous switching. When the switching instants of the controller experience delays with respect to those of the system, a kind of reliable controller design method is proposed, and the dwell time approach is utilized for the stability analysis. Sufficient conditions for the existence of the reliable controller are formulated in terms of a set of LMIs. Then the proposed approach is extended to take into account switched delay systems with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.     

Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching

This paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching, where the switching instants of the controller experience delays with respect to those of the system. A design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures, and the dwell time approach is utilized for the stability analysis. Then the approach is extended to take into account stochastic switched system with Lipschitz nonlinearities and structured uncertainties. Finally, a numerical example is employed to verify the proposed method.     

Exponential synchronization of Markovian jumping chaotic neural networks with sampled-data and saturating actuators

This paper deals with the problem of exponential synchronization of Markovian jumping chaotic neural networks with saturating actuators using a sampled-data controller. By constructing a proper Lyapunov–Krasovskii functional (LKF) with triple integral terms, and employing Jensen’s inequality, some new sufficient conditions for the exponential synchronization of considered chaotic neural networks are derived in terms of linear matrix inequalities (LMIs). The obtained LMIs can be easily solved by any of the available software. Finally, the numerical examples are provided to demonstrate the effectiveness of our theoretical results.     

Robust consensus of nonlinear multi‐agent systems via reliable control with probabilistic time delay

In this paper, the consensus problem of uncertain nonlinear multi‐agent systems is investigated via reliable control in the presence of probabilistic time‐varying delay. First, the communication topology among the agents is assumed to be directed and fixed. Second, by introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time‐varying delay is equivalently transformed into the deterministic time‐varying delay with stochastic parameters. Third, by using Laplacian matrix properties, the consensus problem is converted into the conventional stability problem of the closed‐loop system. The main objective of this paper is to design a state feedback reliable controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed‐loop system is robustly stable in the sense of mean‐square. For this purpose, through construction of a suitable Lyapunov–Krasovskii functional containing four integral terms and utilization of Kronecker product properties along with the matrix inequality techniques, a new set of delay‐dependent consensus stabilizability conditions for the closed‐loop system is obtained. Based on these conditions, the desired reliable controller is designed in terms of linear matrix inequalities which can be easily solved by using any of the effective optimization algorithms. Moreover, a numerical example and its simulations are included to demonstrate the feasibility and effectiveness of the proposed control design scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 138–150, 2016     

Delay‐dependent robust reliable control for uncertain switched neutral systems

This article investigates the robust reliable control problem for a class of uncertain switched neutral systems with mixed interval time‐varying delays. The system under study involves state time‐delay, parameter uncertainties and possible actuator failures. In particular, the parameter uncertainties is assumed to satisfy linear fractional transformation formulation and the involved state delay are assumed to be randomly time varying which is modeled by introducing Bernoulli distributed sequences. The main objective of this article is to obtain robust reliable feedback controller design to achieve the exponential stability of the closed‐loop system in the presence of for all admissible parameter uncertainties. The proposed results not only applicable for the normal operating case of the system, but also in the presence of certain actuator failures. By constructing an appropriate Lyapunov–Krasovskii functional, a new set of criteria is derived for ensuring the robust exponential stability of the closed‐loop switched neutral system. More precisely, zero inequality approach, Wirtinger's based inequality, convex combination technique and average dwell time approach are used to simplify the derivation in the main results. Finally, numerical examples with simulation result are given to illustrate the effectiveness and applicability of the proposed design approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–237, 2016     

Dissipative analysis for discrete‐time systems via fault‐tolerant control against actuator failures

This article investigates the problem of robust dissipative fault‐tolerant control for discrete‐time systems with actuator failures. Based on the Lyapunov technique and linear matrix inequality (LMI) approach, a set of delay‐dependent sufficient conditions is developed for achieving the required result. A design scheme for the state‐feedback reliable dissipative controller is established in terms LMIs which can guarantee the asymptotic stability and dissipativity of the resulting closed‐loop system with actuator failures. In addition, the proposed controller not only stabilize the fault‐free system but also to guarantee an acceptable performance of the faulty system. Also as special cases, robust H_∞ control, passivity control, and mixed H_∞ and passivity control with the prescribed performances under given constraints can be obtained for the considered systems. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed fault‐tolerant control technique. © 2016 Wiley Periodicals, Inc. Complexity 21: 579–592, 2016     

A simple self-triggered sampler for perturbed nonlinear systems

Self-triggered control is a recent design paradigm for resource-constrained networked control systems. By allocating aperiodic sampling instances for a digital control loop, a self-triggered controller is able to utilize network resources more efficiently than conventional sampled-data systems. In this paper we propose a self-triggered sampler for perturbed nonlinear systems ensuring uniformly ultimately boundedness of trajectories. Robustness and time delays are considered. To reduce conservativeness, a disturbance observer for the self-triggered sampler is proposed. The effectiveness of the proposed method is shown by simulation.     

Stability analysis of sampled-data fuzzy controller for nonlinear systems based on switching T–S fuzzy model

This paper investigates the system stability of a sampled-data fuzzy-model-based control system, formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampled-data fuzzy controller has an advantage that it can be implemented using a microcontroller or a digital computer to lower the implementation cost and time. However, discontinuity introduced by the sampling activity complicates the system dynamics and makes the stability analysis difficult compared with the pure continuous-time fuzzy control systems. Moreover, the favourable property of the continuous-time fuzzy control systems which is able to relax the stability analysis result vanishes in the sampled-data fuzzy control systems. A Lyapunov-based approach is employed to derive the LMI-based stability conditions to guarantee the system stability. To facilitate the stability analysis, a switching fuzzy model consisting of some local fuzzy models is employed to represent the nonlinear plant to be controlled. The comparatively less strong nonlinearity of each local fuzzy model eases the satisfaction of the stability conditions. Furthermore, membership functions of both fuzzy model and sampled-data fuzzy controller are considered to alleviate the conservativeness of the stability analysis result. A simulation example is given to illustrate the merits of the proposed approach.     

Memory-based adaptive event-triggered asynchronous tracking control for semi-Markov jump systems with hybrid actuator faults

In this paper, the extended dissipative asynchronous tracking control problem is studied for semi-Markov jump systems with hybrid actuator faults via a memory-based adaptive event-triggered mechanism. Firstly, since the system mode and controller mode do not match exactly, an asynchronous tracking control based on hidden Markov model is designed. Secondly, compared with existing memory-based and memoryless event-triggered mechanisms, the memory-based adaptive event-triggered mechanism proposed in this paper can achieve better performance according to the historical data released and the adaptive event triggering threshold. Next, considering the unsafe operating environment of the device, an asynchronous hybrid actuator failure model is constructed. Furthermore, by designing appropriate Lyapunov–Krasovskii functional, the stochastic stability and extended dissipative performance of the closed-loop system can be guaranteed. Finally, the effectiveness of the proposed method is proved by simulation examples.     

一类动态系统可靠 D -稳定性条件 - LMI方法

考虑一类具有执行器和传感器故障的动力系统可靠鲁棒控制综合问题. 提出了一个系统 D -稳定的充分必要条件. 基于这一充分必要条件, 得到了可靠 H_∞ 控制器存在的条件. 接着用线性矩阵不等式(LMI)方法设计控制器, 使闭环系统当部分控制器件出现故障时鲁棒 D -稳定且具有H_∞性能. 最后通过一个仿真实例说明该文给出的方法及其有效性     

Event-triggered and self-triggered impulsive control for two-time-scale systems

This paper studies the stability problem of two-time-scale system via event-triggered impulsive control and self-triggered impulsive control. The overall system is modeled with the hybrid formalism. Two Chang transformations are introduced to completely decouple the hybrid system states into flow set and jump set. A composite impulsive controller based on slow and fast system states is proposed, under which the slow and fast subsystems are simultaneously triggered by event-triggered and self-triggered mechanism, respectively. As a result, the stability conditions are derived for the system under event-triggered and self-triggered impulsive control, respectively. Furthermore, the theoretical result of self-triggered impulsive control is applied to the consensus of the interconnected two-time-scale systems. Finally, simulation examples and comparison study show the effectiveness of the proposed control strategies.     

Small-gain technique-based adaptive output constrained control design of switched networked nonlinear systems via event-triggered communications

This paper investigates the problem of event-triggered tracking control for switched networked nonlinear systems with asymmetric time-varying output constraints. To handle the output constraints, an output-dependent generic constraint function is constructed to describe relationship between the output and the performance requirement. Meanwhile, an event-triggering rule is designed to reduce communication frequency between the controller and the actuator, thereby reducing the burden of the network communication. Based on the common Lyapunov function method and event-triggered control strategy, an adaptive control method is designed, which can guarantee that the closed-loop signals are bounded and avoid the Zeno behavior. Different from existing results considering constraints, the proposed scheme not only relaxes the restricted condition of constraint boundaries but also both the cases with and without output constraints can be addressed simultaneously. Furthermore, the stability of the system can be guaranteed by the small-gain technique. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed scheme.     

Sampled‐data reliable stabilization of T‐S fuzzy systems and its application

In this article, based on sampled‐data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input‐delay approach, the sampled‐data system is equivalently transformed into a continuous‐time system with a variable time delay. The main objective is to design a suitable reliable sampled‐data state feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger‐based double integral inequality, some new delay‐dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016     

不确定线性系统的最优保性能可靠控制

针对一类不确定线性系统,采用连续增益故障模型提出了考虑执行器故障的保性能可靠控制问题.通过对具有执行器增益故障的系统分析,利用线性矩阵不等式(LMI)分别给出了保性能标准控制、最优保性能标准控制、保性能可靠控制、最优保性能可靠控制存在的充分条件.根据凸优化理论,最优保性能标准控制和最优保性能可靠控制的设计方法转化为一个线性凸优化算法.仿真数例验证了文中所提出方法的可行性.在相同形式的故障发生时,比较最优保性能标准控制与最优保性能可靠控制,进一步说明了最优保性能可靠控制的必要性.     

Quantized control for networked switched systems under denial-of-service attacks via a barrier event-triggered mechanism

This paper studies the quantized control problem for networked switched systems (NSSs) under denial-of-service (DoS) attacks. The quantized state information, together with the switching signal, is transmitted to the controller through a network. In order to reduce communication consumption and controller update frequency, a barrier event-triggered mechanism is utilized to monitor the state at discrete time. Because of the event-triggered mechanism and the DoS attacks on the network, the mismatch between the system mode and the controller mode is thus frequently encountered, which may lead to quantization saturation and system instability. To solve the problem, an update rule is presented for the dynamic quantizer by switching between zooming in and zooming out of the zooming variable, and a feedback controller is proposed with a jointly designed event-triggered mechanism and a dynamic quantizer. Sufficient conditions on the constraints of DoS frequency and duration are obtained to ensure the exponential stability of the switched system. The effectiveness of the obtained results is illustrated by simulation examples and comparative studies.     

Hybrid event-triggered and impulsive control for time-delay systems

In this paper, we study the problem of hybrid event-triggered control for a class of nonlinear time-delay systems. Using a Razumikhin-type input-to-state stability result for time-delay systems, we design an event-triggered control algorithm to stabilize the given time-delay system. In order to exclude Zeno behavior, we combine the impulsive control mechanism with our event-triggered strategy. In this sense, the proposed algorithm is a hybrid impulsive and event-triggered strategy. Sufficient conditions for the stabilization of the nonlinear systems with time delay are obtained by using Lyapunov method and Razumikhin technique. Numerical simulations are provided to show the effectiveness of our theoretical results.     

Stochastic stability and robust control for sampled-data systems with Markovian jump parameters

In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.