H∞ filtering for T–S fuzzy networked systems with stochastic multiple delays and sensor faults
Introduction
It is generally known that the issue of state/signal estimation has been discussed in the areas of control and signal processing. One of the most famous methods is Kalman filtering, which was put forward in [1]. However, it is very difficult to know the knowledge of noises as a prior, which is required in Kalman filtering in some practical systems. In order to solve this problem, filtering approach was introduced. One of the advantages of using filter over Kalman filter is that no distribution characteristic on the noise is needed. Besides, filtering provides stronger robustness over Kalman filtering. Owing to those advantages, much attention has been paid to the filtering, and various results on this topic have been reported in literature (see, e.g., [2], [3], [4], [5], [6], [7], [8], [9], [24], [30], [34] and references there in).
During the past few years, fuzzy systems based on Takagi–Sugeno (T–S) model have been well investigated in [2], [3], [6], [8], [9], [10], [12], [14], [15], [16], [17], [18], [19], [20], [26], [27], [28], [29], [30], [33]. The T–S fuzzy model is made up of a set of local linear models which are smoothly connected by nonlinear fuzzy membership functions. It has been proved that the approach is an efficient one to approximate complex nonlinear systems with arbitrary precision [10]. Recently, some results on the design of filters for T–S fuzzy systems with the approaches based on common quadratic Lyapunov functions have been reported, see, e.g., [11], [13]. However, it has been known that the methods tend to be conservative, and even more, a common quadratic Lyapunov function might not exist especially for highly nonlinear complex systems. In [15], a convex piecewise affine controller design method is proposed based on a new dilated LMI characterization, where the system matrix is separated from Lyapunov matrix such that the controller parametrization is independent of the Lyapunov matrix. In [16], delay-dependent controller has been designed for T–S fuzzy systems based on a switching fuzzy model, and performance is guaranteed by adopting an approach of piecewise Lyapunov function. To reduce the conservatism, stability analysis of fuzzy systems based on the piecewise quadratic Lyapunov functions has been considered in [6], [15]. Similar work can be found in [17], [19], and references therein.
It is well known that one of the most important issues that lead to the systems performance deterioration is time-delay. So far, the stability and filter design problems for networked systems or T–S fuzzy systems with network-induced delays have been investigated by many researchers [11], [13], [19], [20], [21], [22], [23], [24], [26], [27], [31], [32], [33], [34], [36]. In [19], controller for discrete-time T–S fuzzy systems with time-varying state delays has been investigated. A fuzzy controller has been designed for nonlinear impulsive fuzzy systems with time-delay in [20]. Since network delays are usually time-varying and stochastic, recently, the delays have been modeled in various probabilistic ways [21], [22], [23]. On the other hand, packet dropouts have attracted much attention because it may result in the bad performance, and even instability of the system [23], [24], [25]. Robust filtering for a class of nonlinear networked systems with randomly occurring distributed delays, missing measurements and sensor saturation has been discussed in [23], where the occurrence probability of the packet dropout phenomenon obeys an individual and certain probabilistic distribution taking values on 0 and 1. In [24], Dong et al. consider robust fuzzy output feedback control with multiple probabilistic delays and multiple packet dropouts, where the packet dropout phenomenon occurs randomly.
Besides, sensor faults always occur in the practical control systems, which may affect the performance of systems. Therefore, there is a practical interest to consider the sensor faults. Up to now, a great deal of literatures have been reported on the sensor faults [34], [35], [36], [37], [38], [39]. In [37], the control problem of a class of T–S fuzzy systems with stochastic sensor faults has been studied. The fault statistics of each sensor is individually quantified and stochastic sensor faults and non-ideal network quality of services are coupled in a unified framework. To the best of the authors׳ knowledge, the problem of networked filtering for T–S fuzzy systems with stochastic sensor faults, packet dropouts and multiple stochastic time-varying delays being considered simultaneously has not been fully investigated, which motivates us to study on this problem. The main contributions of this paper can be concluded as follows: (i) networked filtering with multiple stochastic time-varying communication delays, stochastic sensor faults and packet dropout phenomena are simultaneously considered in the T–S fuzzy systems framework; (ii) an approach of piecewise quadratic Lyapunov functional is adopted to reduce the conservatism of the results.
By concluding the above discussion, in this paper, our aim is to provide the T–S fuzzy-model-based piecewise filter design for networked control systems, which include multiple stochastic time-varying communication delays, sensor faults and successive data missing phenomenon. Both the sensor faults and packet dropouts in the measurement equation are considered. Moreover, packet dropouts are described by a Bernoulli random process.
The rest of the paper is organized as follows. System descriptions and problem formulations are presented in Section 2. In Section 3, fuzzy filter is designed with piecewise quadratic Lyapunov function. A simulation is conducted to demonstrate that the performance of the system can be guaranteed with the proposed approaches in Section 4 and the conclusion is provided in Section 5.
Notations: The notations throughout the paper are fairly standard. The superscript “T” stands for matrix transpose; denotes the n-dimensional Euclidean space; is the set of all real matrices; and represents identity matrix; and represents zero matrix, respectively. means that P is a real symmetric and positive definite. We use an asterisk to represent a term that is induced by symmetry in symmetric matrices, and stands for a block-diagonal matrix, respectively. and stand for the expectation of x and the expectation of x conditional on y, and and denote the largest and the smallest eigenvalue of the square matrix A, respectively. denotes the space of square-integrable vector functions over .
Section snippets
System descriptions and problem formulations
In this section, we use a T–S fuzzy model to represent the nonlinear physical plant. The measured information received from the plant is transmitted via the shared communication channel, where the sensor faults and the randomly occurring data missing phenomena happen. In what follows, physical plant will be modeled.
Main results
In this section, the problems of performance and filter design for the filtering-error system (14) will be investigated. Theorem 1 Consider the system in (1), and assume the filter parameters Afi, Bfi, Lfi in (14) and attenuation level are given. The filtering-error system in (14) is stochastically stable in the mean square if there exist matrices satisfying the following linear matrix inequality (LMI):where
Illustrative example
In this section, we use an example to illustrate the effectiveness of the filter we proposed. Consider the parameters of the system (14) as follows:
In this example, we choose the following parameters as D=0.1, q=2,
Conclusion
In this paper, the filtering problem for a class of T–S fuzzy system with multiple stochastic time-varying delay, sensor faults and successive packet dropouts has been investigated. The packet dropouts occur randomly and obey the Bernoulli distribution taking on values of 0 and 1. An approach of piecewise quadratic Lyapunov function has been adopted to lessen the conservatism, and it has been proved that the filtering error system is stochastically stable in mean square and performance is
Acknowledgments
This work is supported by the National Natural Science Foundation of China (61272064, 61273026), Shanghai Pujiang Program (14PJ1409000), and Shanghai International Science and Technology Cooperation Project (15220710700) and the Australian Research Council Discovery Project (DP160103567).
Xiaoli Xu received the B.S. degree in automatic control from Lanzhou University of Technology, Lanzhou, China, in 2011. She is currently working toward the M.S. degree in control science and engineering at East China University of Science and Technology, Shanghai, China. Her current research interests include fuzzy systems, networked control systems, and distributed filtering systems.
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2017, NeurocomputingCitation Excerpt :Recently, the Takagi–Sugeno (T–S) fuzzy models [14], which can approximate a great number of nonlinear systems by using a set of local linear models [15], have got a great deal of attention. As a result, many significant results with regard to the T–S fuzzy models have been developed (such as [16,17] and the reference therein), which also include a lot of researches on the FD problems. To mention a few, for a category of uncertain T–S fuzzy systems, a design method of FD filters was proposed in [18].
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2024, IEEE Transactions on Fuzzy SystemsQuantized filtering for networked Takagi–Sugeno fuzzy systems with multipath data packet dropouts
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2020, International Journal of Systems ScienceFinite-time non-fragile filtering for nonlinear networked control systems via a mixed time/event-triggered transmission mechanism
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Xiaoli Xu received the B.S. degree in automatic control from Lanzhou University of Technology, Lanzhou, China, in 2011. She is currently working toward the M.S. degree in control science and engineering at East China University of Science and Technology, Shanghai, China. Her current research interests include fuzzy systems, networked control systems, and distributed filtering systems.
Huaicheng Yan received his B.S. degree in automatic control from Wuhan University of Technology, China, in 2001, and the Ph.D. degree in control theory and control engineering from Huazhong University of Science and Technology, China, in 2007. From 2007 to 2009, he was a Postdoctoral Fellow with the Chinese University of Hong Kong. From June 2011 to August 2011, he was a Research Fellow with the University of Hong Kong. From February 2012 to August 2012, he was a Research Fellow with the City University of Hong Kong. Currently, he is a Professor with the School of Information Science and Engineering, East China University of Science and Technology, Shanghai, China. His research interests include networked control systems, fuzzy systems and multi-agent systems.
Hao Zhang received the B.S. degree in automatic control from Wuhan University of Technology, Wuhan, China, in 2001 and received Ph.D. degree in control theory and control engineering from Huazhong University of Science and Technology Wuhan, China, in 2007. Currently, she is a Professor with the School of Electronic and Information Engineering, Tongji University, Shanghai, China. From December 2011 to December 2013, she was also a Postdoctoral Fellow with the City University of Hong Kong, Kowloon, Hong Kong. Her research interests include complex network, network based control systems, multi-agent systems and switching systems.
Fuwen Yang received the Ph.D. degree in control engineering from Huazhong University of Science and Technology, China, in 1990. He is currently an Associate Professor with Griffith School of Engineering at Griffith University, Australia. He was a Research Fellow with Brunel University and King׳s College London, UK, a Professor with Fuzhou University and East China University of Science and Technology, China, and an Associate Professor with Central Queensland University, Australia. He had also held Visiting Professor positions with the University of Manchester, UK, and the University of Hong Kong, China. He is an Associate Editor on the IEEE CSS Conference Editorial Board and a Senior Member of IEEE. He has published more than 200 journal and conference papers. His main research interests include networked control systems, distributed filtering and sensing, reliable fault detection and diagnosis, distributed control and filtering for smart girds, and solar PV power generation systems.