Improved event-triggered control for networked control systems subject to deception attacks
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 filter design problem is addressed in [23] for neural networks subject to deception attacks. In [24], the authors study the finite-time event-triggered 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: is the -dimensional Euclidean space, and is the set of all real matrices. and are the identity matrix and the zero matrix, respectively. and denote the sets of nonnegative and positive integers, respectively. is a symmetric and positive (negative) definite matrix. is the Euclidean norm. The superscripts “” and “” are the matrix transposition and the matrix inverse, respectively, and denotes . The symbol “” is the matrix entry implied by symmetry. denotes the diagonal matrix of corresponding entries, and is the column vector . is the expectation operator.
Section snippets
System description
Consider the following linear continuous-time system:where is the system state, is the system input, and and are known constant matrices. Assume that there exists a controller gain such that 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:Now we will show that the maximum upper bound of 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)
- et al.
control for network-based systems with time-varying delay and packet disordering
J. Frankl. Inst.
(2011) - et al.
Stabilization of linear systems over networks with bounded packet loss
Automatica
(2007) - et al.
Reliable control for networked control systems with probabilistic actuator fault and random delays
J. Frankl. Inst.
(2010) - et al.
Distributed event-triggered control for networked control systems with stochastic cyber-attacks
J. Frankl. Inst.
(2019) - et al.
A state-feedback approach to event-based control
Automatica
(2010) - et al.
Event-driven observer-based output feedback control for linear systems
Automatica
(2014) - et al.
Reliable output control of nonlinear systems with dynamic event-triggered scheme
J. Frankl. Inst.
(2019) - et al.
Event-triggered control for active vehicle suspension systems with network-induced delays
J. Frankl. Inst.
(2019) - et al.
Improved approaches on adaptive event-triggered output feedback control of networked control systems
J. Frankl. Inst.
(2018) - et al.
An improved memory-event-triggered control for networked control systems
J. Frankl. Inst.
(2019)
On scheduling of deception attacks for discrete-time networked systems equipped with attack detectors
Neurocomputing
Hybrid-driven-based filter design for neural networks subject to deception attacks
Appl. Math. Comput.
A new approach to event-triggered static output feedback control of networked control systems
ISA Trans.
Static output feedback stabilization of networked control systems with a parallel-triggered scheme
ISA Trans.
Event-triggered stabilization of neural networks with time-varying switching gains and input saturation
IEEE Trans. Neural Netw. Learn. Syst.
Markov jump linear systems with switching transition rates: mean square stability with dwell-time
Automatica
Improved delay-range-dependent stability criteria for linear systems with time-varying delays
Automatica
Wirtinger-based integral inequality: application to time-delay systems
Automatica
An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay
Automatica
Sampled-data output feedback control based on a new event-triggered control scheme
Inf. Sci.
Improved inequality-based functions approach for stability analysis of time delay system
Automatica
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2022, Journal of the Franklin InstituteCitation Excerpt :NCSs have many applications, such as geological exploration, automated manufacturing [1,2], remote surgery [3], reconnaissance, unmanned aerial vehicles, electrification, and other fields because of its low cost and flexible operation. However, there still exist many challenging problems with NCSs due to such factors as external disturbances and bandwidth limitations, which have attracted the extensive effort among the research community of this area [4–9]. This paper is organized as follows: Section 2 presents the system and the background.