Elsevier

Fuzzy Sets and Systems

Volume 452, 10 January 2023, Pages 91-109
Fuzzy Sets and Systems

Dynamic event-triggered security control for networked T-S fuzzy system with non-uniform sampling

https://doi.org/10.1016/j.fss.2022.08.018Get rights and content

Abstract

This paper is focused on the security control problem for the dynamic event-triggered networked T-S fuzzy control system with non-uniform sampling and stochastic network attacks. Different from existing research, the signals from sensor are sampled in a non-uniform period. To improve communication, a novel dynamic event-triggered method is proposed, which can adjust the trigger parameters dynamically according to the changes of external output. Then, a T-S fuzzy dynamic output feedback control model with event-triggered mechanism and network attacks is constructed. Furthermore, by introducing a set of slack matrix, the asynchronous premise variable problem caused by event-triggered method is solved, and some sufficient conditions that insure the asymptotic stability with an H performance requirement of the established closed-loop system can be obtained by utilizing Lyapunov function method and stochastic analysis technique. Moreover, the gains of the fuzzy dynamic output feedback controllers are found by solving the linear matrix inequalities (LMIs). Finally, two practical examples are given to support the merits and effectiveness of the proposed method.

Introduction

With the rapid development of network technology, networked control systems (NCSs) have attracted lots of scholars owing to their superiority on low cost and high reliability in installation and control. A large amount of related literature have been published in process control, such as H control [1], [2], [3], [4], finite-time control [5], [6], [7], [8], output feedback control [9], [10], [11], [12], etc. Among these control methods, many networked control systems model can not easily deal with nonlinear problems. It makes the analysis and synthesis more difficult. Therefore, Takagi-Sugeno (T-S) fuzzy model is introduced and much research has paid lots of attention in the past few decades. In essence, T-S fuzzy approach is to divide nonlinear dynamic systems into a series of linear sub-systems through IF-THEN rules, and combine a set of linear models to approximate the original nonlinear systems through nonlinear membership functions. Therefore, many scholars attempt to utilize T-S fuzzy approach and give the stability criteria of nonlinear systems by establishing the Lyapunov functions. For instance, the authors in [13] investigated the problem of quantization control for networked cascade systems with event trigger and random network attacks via T-S fuzzy approach. The authors in [14] are concerned with the security control with an H performance requirement for the T-S fuzzy networked systems.

Noticeably, most of the available results are concerned about networked control systems without considering the influence of external disturbance. In fact, external disturbance and nonlinearity always exist in the practical installation. To cope with these issues, the authors in [15] investigated the problem of passivity-based robust control for Markovian jump systems and designed time-dependent state feedback sampled-data controllers under a novel stochastic sufficient passivity criteria. The authors in [16] investigated the H output tracking control problem by proposing a novel adjusted event-triggered scheme. Most recently, the authors in [17] researched the effect of the external disturbances on the networked stochastic system in a unified performance index. Furthermore, it is well known that not all the state variables of systems are available for controller implementations in practical control systems. Therefore, it is necessary to design output feedback control strategies such as observer-based control and dynamic output feedback control. Compared with the static feedback control, the dynamic output feedback control method can obtain less conservatism at the cost of increasing computational burden [18]. Recent years, a large amount of achievements have been published for networked control systems [19], [20], [21]. Despite the fact, in regard to event-based T-S fuzzy networked systems, the co-design of event-triggered scheme and dynamic output feedback controller has not paid enough attention.

Meanwhile, with the expansion of network scale, it is noticed that some issues need to be considered to improve the limitation of communication bandwidth. Therefore, an event-triggered mechanism (ETM) is proposed to reduce the number of unnecessary information in the transmission process. When the signals are sampled with a constant period, the event-triggered mechanism will judge whether the signal needs to be updated. Compared to the existing time-triggered mechanism, the proposed event-triggered mechanism can release the data in a lower rate and obtain a better control performance. By now, the event-triggered mechanism has gained much attention and lots of the literature have been published [22], [23], [24], [25], [26]. However, it is difficult to adapt to the change of external and internal environment if the event-triggered threshold parameter is a constant. An effective method is proposed to solve this issue, which can be generally summarized as the following two types: the adaptive event-triggered mechanism (AETM) and the dynamic event-triggered mechanism (DETM). For example, the authors in [27] proposed an improved event-triggered scheme to design the control for networked cascade system. The authors in [28] devised an improved dynamic event-triggered mechanism to deal with the problems of fault detection and isolation. In recent years, the control issue of DETM has been widely concerned by scholars in [28], [29], [30], [31]. However, there have been very few results on dynamic event-triggered fuzzy networked systems, so it is worth taking further investigation by modeling a general dynamic event-triggered mechanism with more flexibility of parameters. On the other hand, the signals are usually sampled at a regular period in the most sampled control system. However, in practical applications, due to the influence of the sporadic sensor faults and network loads, the sampling period may not be a constant. Besides, for the sake of saving network bandwidth resource, it is more convenient to schedule via a non-uniform sampling scheme if there are multiple systems to transmit data on a shared communication network. Although some scholars have studied the problem of non-uniform sampling [32], [33], [34], there are still few results on dynamic event-triggered mechanism with non-uniform sampling. Thus, it is necessary to investigate the non-uniform sampling strategy instead of the periodic sampling. Inspired by the literature [28], [29], [30], [32], [33], [34], [35], we currently establish a DETM with non-uniform sampling strategy to investigate the control problems of T-S fuzzy networked system.

Although communication networks provide many advantages for networked system, at the same time they also bring some issues owing to the openness of communication networks, such as denial-of-service (DoS) attacks [36], [37], deception attacks [38], [39] and so on. The DoS attacks will prevent the information from reaching the controller, while the deception attacks get the information of communication network systems by injecting deception information into the data-communication channel. Therefore, the security issue of the control system under network attacks has attracted much attention and some effective methods have been proposed to cope with network attacks. For instance, the authors in [40] addressed the consensus of leader-following multiagent system with network attacks and semi-Markovian switching topologies. The authors in [41] introduced distributed event-triggered mechanism to design the H filter of complex sensor networks with network attacks and sensor saturations. To deal with the influence of stochastic deception attacks, the authors in [42] are concerned with the design of event-based filter for networked control system in the sense of finite-time boundedness. By taking the deception attacks into account, it is desired to address state output feedback control of event-based T-S fuzzy systems.

Inspired by the views above, this paper focuses on the dynamic event-triggered security control for networked T-S fuzzy system with non-uniform sampling and network attacks. The main contributions of this paper are summarized as follows: (1) A novel dynamic event-triggered strategy with non-uniform sampling is constructed to advantage a significant reduction of the signals communication burden. (2) The dynamic output feedback fuzzy controllers are first designed for the networked T-S fuzzy system with non-uniform sampling and network attacks. (3) Asynchronous premise variable problems caused by sampled-data-based event-triggered method are solved by employing a set of slack matrix, and some sufficient conditions are derived to ensure the asymptotic stability with H performance of the established closed-loop system. Meanwhile, the parameters of the dynamic output feedback fuzzy controllers are obtained by LMIs methods.

The rest of this paper is presented as follows: in Section 2, dynamic event-based T-S fuzzy system models with network attacks are established. A set of sufficient conditions and event-based fuzzy dynamic output feedback controller are presented in Section 3. Two practical examples are given in Section 4, and a concise conclusion is drawn in Section 5.

Notation: Rn and Rn×m stand for the n-dimensional Euclidean space and the set of n×m real matrix respectively; the superscript AT represents transposition of the matrix A, while A1 is the inverse of the matrix A; col{A,B} denotes the column vector A and B with appropriate blocks; diag{} denotes the block-diagonal matrix; B>0(0) stands for a positive definite (positive semi-definite) matrix; E{Y} represents mathematical expectation of stochastic variable Y; The notation ⁎ represents the symmetric term in symmetric block matrices.

Section snippets

Problem statement and modeling

The framework of the dynamic event-triggered networked T-S fuzzy control system with non-uniform sampling and stochastic network attacks is shown in Fig. 1.

Main results

Before proceeding further, an assumption and some lemmas are proposed to facilitate obtaining the results.

Assumption 1

[43] The nonlinear deception attacks functions f() is continuous and satisfies the following condition.f(y(t),t)2Fy(t)2, where F is a real constant matrix.

Lemma 1

For all t[ak,ak+1) and given initial value θ(0)0 in (4), if the parameters α1, α2, α3, σ1, σ2 satisfy 0<σ1σ2, 0α1α3 and α2>0, then, the auxiliary variable θ(t)0 holds.

Proof

From (4), for the all t[ak,ak+1), we haveσ1θ(t)+α1(ek(t)+y

Simulation example

In this section, two practical examples are given to verify the effectiveness of the designed method with the dynamic event-triggered mechanism and network attacks.

Example 1

Consider a tunnel diode circuit system [44], which is presented as{Cx1˙(t)=iD(t)+x2(t),Lx2˙(t)=x1(t)Rx2(t)+u(t)+w(t),z(t)=x1(t)+w(t),y(t)=x1(t), where iD(t) is the diode function, x1(t) and x2(t) are the system state variables, z(t) is the controlled output, y(t) is the measurement output variables, u(t) and w(t) are the control

Conclusion

The dynamic event-based output feedback control for networked T-S fuzzy system with non-uniform sampling and stochastic network attacks is investigated in this paper. A novel dynamic event-triggered mechanism under non-uniform sampling has been developed, which is more applicable in the practical control systems and will be a higher utilization of the network resources. Taking account of these influence, a closed-loop system based on T-S fuzzy dynamic output feedback controllers is constructed.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No. 62022044, No. 61873107, No. 61973152), in part by the Jiangsu Natural Science Foundation for Distinguished Young Scholars (No. BK20190039).

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