Improved event-triggered control for networked control systems subject to deception attacks

https://doi.org/10.1016/j.jfranklin.2020.12.018Get rights and content

Abstract

This paper investigates the event-triggered control problem for networked control systems subject to deception attacks. An improved event-triggered scheme is proposed to reduce transmission rate by using both the information of the relative error and the past released signals. Under the proposed event-triggered scheme, a new switched time-delay system model is proposed for the event-triggered control systems. Based on the new model, the exponential mean-square stability criteria are derived by using the constructed Lyapunov function. Then, a co-design method is developed to obtain both trigger parameters and mode-dependent controller gains. Finally, the proposed scheme is verified by an unmanned aerial vehicle system.

Introduction

Networked control systems (NCSs) are a class of systems exchanging information among system components through a communication network [1]. The control problems of NCSs have attracted substantial attention [2], [3], [4], [5], [6], [7]. Most of these results use a time-triggered scheme. In time-triggered NCSs, the control signals are updated under a fixed ratio. However, under the time-triggered scheme, many redundant signals are transmitted. To reduce transmission rate, event-triggered schemes (ETSs) are adopted for NCSs [8], [9].

In event-triggered NCSs, the sampled signals are transmitted only when event-triggered conditions are violated [8], [9], [10]. Recently, the fruitful theoretical results have been derived under various ETSs [9], [11], [12], [13], [14], [15], [16], [17], [18], [19]. In terms of triggered conditions, these common ETSs can be classified into two types: the absolute and the relative ETSs. In the absolute ETSs, the absolute error information are used. Specifically, the authors of [12] proposed an absolute ETS by using a constant threshold. To reduce transmission rate at the transient process, an absolute ETS is proposed in [13] based on an exponentially decreasing threshold. Conversely, the event generators in the relative ETSs use the relative error information [9], [15], [16], [17], [18], [19], [20]. To be specific, a continuous ETS is proposed in [17]. The continuous ETS may not exclude Zeno behavior [21]. To exclude Zeno behavior, a periodic ETS for linear NCSs is proposed in [9]. The above ETSs uses the present sampled signals information only. In [19], a memory-based ETS is proposed by using the past released signals information to improve system performance. However, the ETS in [19] increases the number of trasnmitted signals. From the above discussion, though the results in [9], [15], [16], [17], [18], [19] are elegant, the design of the ETS still has room for further improvement. How to propose an improved ETS for NCSs to further reduce transmission rate is significant.

In the event-triggered NCSs, the networked infrastructures and devices are prone to be corrupted by potential cyber attacks. Cyber attacks are caused by the malicious attackers. According to the attack targets, there are three types of cyber attacks: Denial of Service (DoS) attacks, replay attacks and deception attacks [22]. DoS attacks can block the communication channel. Replay attacks may replace the transmitted signals by the past signals. Deception attacks can reconstruct the transmitted signals by malicious attack signals. One of the most important attack modes on the network security is the deception attacks. With the rapid development of network, the risks of deception attacks cannot be ignored. The control problems subject to deception attacks have attracted significant attention [22], [23], [24]. For example, the attack scheduling problem is investigated in [22] for a class of stochastic linear systems. Based on the deception attacks proposed in [22], the hybrid-driven-based H filter design problem is addressed in [23] for neural networks subject to deception attacks. In [24], the authors study the finite-time event-triggered H filter design problem for a NCS subject to stochastic deception attacks. Thus, how to establish a system model under the improved ETS subject to deception attacks is meaningful.

Motivated by the above discussions, this paper investigates the improved event-triggered control problem for NCSs subject to deception attacks. The following difficulties are required to be solved: Firstly, how to propose an improved ETS to further reduce transmission rate is challenging. To overcome this difficulty, an improved ETS is proposed in this paper by using both the information of the relative error and the past released signals. The proposed ETS consists of two trigger conditions. Secondly, the sojourn time of the system staying in which condition may be unknown. Then, the approaches in [9], [13], [25], [26] cannot be applicable to our case. To overcome this difficulty, we develop a common Lyapunov function for the switched system. By employing Lyapunov stability theory, sufficient conditions are derived for exponential mean-square stability by means of linear matrix inequalities (LMIs). The main contributions of this paper are summarized as follows: Firstly, an improved ETS is proposed for NCSs, which further reduces transmission rate compared to the existing ETSs. Secondly, a new switched time-delay model is presented for the event-triggered NCSs subject to deception attacks. Thirdly, based on the constructed Lyapunov function, new sufficient conditions are derived for exponential mean-square stability and controller design.

Notation: Rn is the n-dimensional Euclidean space, and Rm×n is the set of all m×n real matrices. Im and 0m×n are the m×m identity matrix and the m×n zero matrix, respectively. N0 and N+ denote the sets of nonnegative and positive integers, respectively. X>0 (X<0) is a symmetric and positive (negative) definite matrix. · is the Euclidean norm. The superscripts “T” and “1” are the matrix transposition and the matrix inverse, respectively, and He(X) denotes (X+XT). The symbol “” is the matrix entry implied by symmetry. diag{X1,,Xn} denotes the diagonal matrix of corresponding entries, and col{x1,,xn} is the column vector [x1T,,xnT]T. E is the expectation operator.

Section snippets

System description

Consider the following linear continuous-time system:x˙(t)=Ax(t)+Bu(t)where x(t)Rn is the system state, u(t)Rm is the system input, and A and B are known constant matrices. Assume that there exists a controller gain K such that A+BK is Hurwitz.

Fig. 1 demonstrates the framework of an event-triggered NCS. The system states are sampled periodically. To save communication cost, an improved ETS is proposed. Under the ETS, the system is controlled over the networks subject to deception attacks.

Improved ETS

Event-triggered control under the improved ETS

In this section, sufficient conditions are established for the closed-loop system (23) to be exponentially stable in the mean-square sense. Then, a controller design method is developed.

Illustrative examples

In this section, Example 1 is used to show the superiority of Corollary 1 and the effectiveness of different control gains. In addition, Example 2 is used to show the effectiveness of the proposed ETS (5). Moreover, the comparison with the result in [9] is given.

Example 1

Consider the system (1) investigated in [9] with the following parameters:A=[010000100001001030],B=[01100130]Now we will show that the maximum upper bound of τM by applying Corollary 1 is larger than that by using Theorem 1 in [9]. To

Conclusions

In this paper, the event-triggered control problem was investigated for networked control systems subject to deception attacks. An improved event-triggered scheme was proposed. Under the event-triggered scheme, a new switched time-delay system model was proposed. The criteria were derived to guarantee exponential mean-square stability of the switched system. The co-design method was given to obtain both trigger parameters and mode-dependent controller gains. Finally, an unmanned aerial vehicle

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.

Acknowledgments

This work was supported by National Natural Science Foundation of China under Grant 61773357 and 71532008.

References (43)

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