A random-switch-surface based neural sliding mode framework against actuator attacks of delayed singular semi-Markov jump systems

This article addresses the challenge of actuator attacks in delayed singular semi-Markov jump systems (singular S-MJSs) with uncertainties and exogenous disturbances, operating under conditions of partially unknown transition rate (PUTR) matrix and completely unknown transition rate (CUTR) matrix, respectively. The specifics of actuator attacks and the bounds of disturbances remain elusive during the controller design process. Furthermore, any information regarding unknown elements within the PUTR/CUTR matrix is unattainable. To stabilize systems against actuator attacks, we introduce a distinctive “random switch”-triggered sliding surface, referred to as the random switch surface (RSS). Additionally, H_∞ stochastic admissibility sufficient conditions are established under PUTR and CUTR matrices, respectively. Two corresponding algorithms are presented, leveraging solvable linear matrix inequalities (LMIs), to determine the gain matrices. Further, an innovative adaptive H_∞ neural sliding mode control (SMC) law is conducted, incorporating an ingenious neural network to approximate actuator attacks. It also enables real-time estimation of unavailable parameter bounds. Finally, we conduct simulations on several examples using our proposed method, as well as other comparison methods, to demonstrate the effectiveness of the proposed approach.