Dynamic event-triggered control for networked control systems under deception attacks: a switching method
Introduction
Networked control systems (NCSs) are a type of control system in which the controller, actuator, and sensor exchange information via a network [1]. Fruitful results have been established to investigate the control problems of NCSs [2], [3], [4], [5], [6]. A time-triggered scheme is adopted in these results. Under a time-triggered scheme, signals are sent at a given ratio. However, several unnecessary signals are transmitted. To reduce the number of transmitted signals (NTSs) for NCSs, event-triggered schemes (ETSs) have been used [7].
In event-triggered systems, when conditions are violated, the system measurements are transmitted [8], [9]. Recently, several results have been derived in [10], [11], [12], [13], [14], [15], [16], [17]. Specifically, a continuous state-dependent ETS is presented in [10]. Zeno behavior cannot be avoided in this continuous ETS [18]. By using the sampled-data approach to exclude Zeno behavior, a periodic ETS is proposed for linear NCSs in [11]. However, continuous system information can be used to enhance control performance. Selivanov et al. [13] propose a switching ETS by introducing a waiting time. In the aforementioned studies, static ETSs are used. To further reduce the NTSs, dynamic ETSs have been proposed by using additional dynamic variables. Under dynamic ETSs, the control performance is almost the same as those of the static forms, and the NTSs can be reduced. In particular, dynamic ETSs have been investigated for NCSs in [19] and cyber-physical systems in [20], [21]. Based on the dynamic ETS, the fault-tolerant control problem is investigated in [22], [23]. However, in the above studies, the values of the trigger parameters cannot be larger than the maximum allowed value subject to conditions for system stability. Therefore, proposing a new ETS to overcome this limitation is significant and challenging.
In event-triggered NCSs, networked devices are likely to be corrupted by cyber attacks. Cyber attacks may destroy system stability and even threaten people [24], [25]. Cyber attacks can be classified into three types: replay attacks, denial of service attacks, and deception attacks [26], [27]. Network security can be severely damaged by deception attacks. By substituting the system states with malicious attack signals, attackers corrupt the system states. Control problems under deception attacks have attracted substantial attention [28], [29], [30]. For example, Liu et al. [28] address the filter design problem subject to deception attacks. Based on a memory-based ETS, Wang et al. [30] consider the control problem for NCSs under stochastic deception attacks.
Motivated by the above discussion, we propose a dynamic switching ETS for NCSs under stochastic deception attacks. Then, sufficient criteria are derived to guarantee the exponential mean-square stability for the investigated system with performance. Linear matrix inequalities (LMIs) techniques are applied. Finally, an unmanned aerial vehicle (UAV) system is used to validate the availability of the proposed dynamic ETS. The primary contributions of the study are summarized as three aspects: First, a dynamic switching ETS is presented for NCSs to reduce the NTSs. The dynamic ETS presented in this study is a generalization of the static ETS in [13]. Second, a switched model is developed for dynamic event-triggered systems under stochastic deception attacks. Third, we investigate the control problem under the dynamic switching ETS. By utilizing the constructed Lyapunov function, novel sufficient criteria are established for exponential mean-square stability and performance.
Notations: The n-dimensional Euclidean space is represented by . The sets of non-negative and positive integers are represented by and , respectively. denotes a positive (negative) definite matrix. The matrix inverse and matrix transposition are represented by the superscripts “” and “T”, respectively. , and represent the m-order identity matrix, m-order zero matrix, and zero matrix, respectively. denotes is the diagonal matrix of the corresponding entries, and is denoted by . The expectation operator is denoted by , the Euclidean norm is denoted by , and . denotes the length of the interval . “” represents the symmetric matrix entry.
Section snippets
System to be investigated
The linear system to be investigated is described as:where is the system state, is the system disturbance, and is the system input. In addition, , and F are given constant matrices. We assume that the system (1) can be stabilized.
Based on the ETS, the structure of a NCS under stochastic deception attacks is shown in Fig. 1. To reduce the NTSs, a dynamic switching ETS is proposed in this study. The communication networks suffer from stochastic
Dynamic switching event-triggered control
In this section, novel criteria are provided to guarantee the exponential mean-square stability of the dynamic event-triggered system (8). Then, the co-design approach is given, and the smallest inter-event time is also analyzed.
Illustrative examples
Next, an UAV system is utilized to validate the effectiveness of the dynamic ETS (4). Moreover, a comparison with the static ETS in [13] is provided. Example 1 Consider the UAV system (1) investigated in [8]: Moreover, the terminal time of the simulation is s, , and the disturbance is described as
Conclusions
Based on the ETS, the control problem was addressed for NCSs subject to stochastic deception attacks. A new dynamic switching ETS was proposed. Under the proposed scheme, a novel switched system model was presented under stochastic deception attacks. The criteria were derived to guarantee performance and exponential mean-square stability. The co-design method was presented. Finally, UAV system was utilized to demonstrate the effectiveness of dynamic ETS.
CRediT authorship contribution statement
Zhiying Wu: Conceptualization, Methodology, Software, Validation, Writing - original draft, Writing - review & editing. Junlin Xiong: Conceptualization, Investigation, Project administration, Supervision, Writing - review & editing. Min Xie: Methodology, Project administration, Supervision.
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 partially supported by Research Grant Council of Hong Kong under CityU 11203519, and partially by National Natural Science Foundation of China under Grant Nos. 71971181 and 61773357.
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