Reliable control for hybrid-driven T–S fuzzy systems with actuator faults and probabilistic nonlinear perturbations

Abstract

This paper is concerned with the reliable controller design for hybrid-driven nonlinear systems via T–S fuzzy model with probabilistic actuator faults and probabilistic nonlinear perturbations. To reduce unnecessary transmissions in the network, a hybrid-driven scheme is introduced, in which the communication transmission scheme can be selected between time-driven scheme and event-driven scheme. The switch law of the communication schemes is modeled as Bernoulli distributed stochastic variable. Considering the network-induced delay, nonlinear perturbations and the probabilistic actuator faults, a new model is constructed under the hybrid driven scheme. By using Lyapunov–Krasovskii functionals and stochastic analysis techniques, sufficient conditions are established which ensure the asymptotical stability of the augmented system under hybrid driven scheme. Furthermore, a unified co-design algorithm for the desired controller and the hybrid-driven scheme are developed. Finally, a typical simulation example is used to demonstrate the validity of obtained results.

Introduction

During the past few years, fuzzy systems based on Takagi–Sugeno (T–S) model have been widely recognized as an efficient approach to approximate nonlinear systems with arbitrary precision. Research in modeling and control of nonlinear systems by T–S fuzzy model has received a great deal of attention, because they can be analyzed by the linear system theories and described by a family of IF-THEN rules. There are some outstanding results reported [1], [2], [3], [4], [5], [6], [7], [8], [9]. In [1], the authors concentrate on the fault detection filtering problem for nonlinear switched stochastic system in the T–S fuzzy framework. In [3], the authors investigate network-based output tracking control for a T–S fuzzy system that cannot be stabilized by a non-delayed fuzzy static output feedback controller. The authors study the distributed event-triggered H_∞ filtering for a class of nonlinear system in [5]. The authors investigate the reliable filter design with strict dissipativity for a class of T–S fuzzy time-delay systems in [9]. It should be observed that the premises in the controlled fuzzy plant and the one in the fuzzy controller are often asynchronous due to the presence of network-induced delays. How to deal with the asynchronous premises in networked control systems is still an open problem. The existing results are not enough, more effort should be paid to deal with this problem, which motivates the present investigation.

Due to the increasing number of components in practical systems, the presence of actuator faults is unavoidable, which may result in deterioration of system performance and even instability of the closed-loop system. Therefore, it is essential and significant to increase system reliability and security. The studies of reliable control scheme have received considerable attention of control community and lots of outstanding results have been obtained [10], [11], [12]. In [10], the problem of adaptive fault tolerant tracking controller for a class of uncertain nonlinear systems with input quantization and actuator faults is investigated. In [11], the fault-tolerant stabilization problem has been studied for a class of nonlinear systems with uncertain parameters. The authors in [12] deal with the problem of reliable and robust H_∞ static output feedback controller synthesis for continuous-time nonlinear stochastic systems with actuator faults. Despite these efforts, the reliable control for T–S fuzzy systems with probabilistic nonlinear perturbation under hybrid-driven scheme has not drawn any attention in the present literature.

Networked control systems have become an active research area in recent years due to the advantage of simple installation, low cost, easier maintenance, etc. However, the introduction of communication networks can bring some problems. Especially, due to the limited network bandwidth, the phenomena of time delay, packet dropout and noise interference are often encountered, which may lead to performance degradation and system instability. Fortunately, much effort has been made on how to reduce the amount of network transmission and improve the efficient of network utilization. Different strategies have been proposed in the existing publications [13], [14], [15], [16], [17], [18], [19], [20]. Generally speaking, the researches tackling with this problem can be classified into two categories:(i) The first one is the time-driven scheme. With this method, network transmission is assigned periodically. The fixed sampling interval is chosen to guarantee a desired performance under the worst conditions such as external disturbances, uncertainties, time-delays and so on. However, when a control system runs in a steady state, there is no need to update the measurement and control signal, such a method will lead to unnecessary waste of network resources. (ii) The second one is the event-driven scheme. In order to overcome the drawback of the time-driven scheme, the event-driven scheme has been proposed in [19], in which the task is executed only when the pre-defined condition is satisfied. The event-driven scheme has been proved to be an effective way in saving the network resource while maintains satisfactory system performance. The main advantages of the event-driven scheme can be summarized as low transmission frequency, reduction in the release times of the sensor and reduction in calculation cost of controller. Recently, on the basis of the work in [19], different problems have been investigated under different event-driven schemes [13], [14], [15], [16], [17], [18], [20]. For example, the authors in [13] investigate decentralized control for a class of interconnected system. In [17], the authors are concerned with H_∞ filter design for a class of neural network systems with event-triggered communication scheme and quantization.

Different from above works, taking the random actuator faults and probabilistic nonlinear perturbations into consideration, the reliable control for hybrid-driven T–S fuzzy systems is investigated in this paper. Compared with some past works, the adopted hybrid-driven scheme pays attention to the variation of the network loads, which is more flexible in saving the network resources. In our hybrid-driven scheme, a Bernoulli distributed stochastic variable is used to describe the access status of time-driven scheme and the event-driven scheme. Such a method is suitable to guarantee the desired performance of networked control systems under the worst conditions of external disturbances, uncertainties, time-delays and so on. The hybrid-driven scheme is also capable of improving the network resources utilization while maintaining satisfactory system performance especially when there is no negligible measurement variation.

However, to the best of our knowledge, no investigations have been involved about the problem of reliable control for hybrid-driven T–S fuzzy systems with probabilistic nonlinear perturbations under hybrid-driven scheme. Compared with the existing researches, the reliable control is firstly addressed for hybrid-driven T–S fuzzy systems with random actuator faults and probabilistic nonlinear perturbations. The main contributions of this paper are as follows: (1) A Bernoulli distributed stochastic variable is used to describe the switch between different communication schemes in the hybrid-driven scheme, which is efficient to make full use of the network capacity. (2) Considering the actuator faults, probabilistic nonlinear perturbations and network-induced delays, a new model is established under the proposed hybrid-driven scheme. (3) Based on the model, sufficient conditions are obtained to ensure the desired system performance and the explicit design method of controller gains are derived. (4) The premises in the controlled plant and the one in the fuzzy controller operate in an asynchronous way in this paper.

The rest of this paper is organized as follows. In Section 2, the issue on the implementation of the hybrid-driven scheme is presented. Section 3 gives the sufficient conditions for the stabilization of the augmented system. Furthermore, the explicit controller design method is presented. An illustrative example is provided in Section 4 to show the effectiveness of the obtained results. Finally, Section 5 concludes the paper.

Notation: ${\mathbb{R}}^n$ and ${\mathbb{R}}^{n\times m}$ denote the n-dimensional Eculidean space, and the set of n × m real matrices; the superscript T stands for matrix transposition; I is the identity matrix of appropriate dimension; the notation X > 0(respectively, X ≥ 0), for $X\in {\mathbb{R}}^{n\times n}$ means that the matrix X is real symmetric positive definite (respectively,positive semi-definite); Prob{X} denotes probability of event X to occur; Sym{X} denotes the expression $X^T+X$; $\mathcal{E}$ denotes the expectation operator; for a matrix B and two symmetric matrices A and C, $\left[\begin{array}{cc}A& *\\ B& C\end{array}\right]$ denotes a symmetric matrix, where * denotes the entries implied by symmetry.