Optimal resilient tracking control of switched systems under denial-of-service attacks

This article investigates the optimal output tracking problem for linear switched systems under DoS attacks. In contrast to early results which only consider the stability of switched systems under DoS attacks, the proposed control scheme can ensure the stability of the system while optimizing the system performance. Firstly, an augmented system is constructed based on the physical objects and command generator. Then, a Riccati equation of such an augmented system with DoS attacks is provided, and the optimal control scheme is obtained by iterative algorithm. Furthermore, to better align with practical scenarios, in this article, some restrictions on the instants of DoS attacks and switchings are removed, that is, multiple switchings are allowed during both active and inactive intervals of DoS attacks. In addition, the quantitative relationship regarding the duration and frequency of DoS attacks and the switching law is provided, which plays a key role in ensuring the stability of switching system under attacks. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method. •The design method of this article can not only ensures the stability of the switched system under DoS attacks but also optimizes the system performance.•Due to the consideration of DoS attacks, the Riccati equation derived includes an attack probability ᾱ, which may affect its solution’s existence and uniqueness. To ensure system stability, the influence of ᾱ is analyzed, and an upper bound for ᾱ is provided. The uniqueness of the solution is further proven through an iterative algorithm.•Compared with previous studies, which restricted the number of system switchings during the DoS attack interval, this paper explores a more general scenario where multiple system switchings are permitted during both the DoS attack active and inactive intervals.•A relationship between the average dwell time of subsystems and the frequency and duration of DoS attacks is provided, which plays a key role in ensuring the stability of the system.