Dynamic-Event-Based Reachable Set Synthesis for Nonlinear Delayed Hidden Semi-Markov Jump Systems Under Multiple Cyber-Attacks

In this article, the problem of reachable set (RS) synthesis for a class of nonlinear delayed hidden semi-Markov jump systems with actuator saturation and multiple cyberattacks is addressed. First, a dynamic-event-triggered mechanism (DETM) with a time-varying additional threshold is introduced, which can save communication resources more effectively. However, due to the introduction of DETM, the modes of the controller and the system exhibit asynchronous behavior. On the other hand, while network communication facilitates signal transmission, it also exposes the system to an open environment vulnerable to cyberattacks. To address these issues, we devise a security asynchronous controller based on the hidden Markov model. In addition, this article also considers a class of actuator saturation problem. After that, the sufficient conditions for RSs are obtained by applying the stability theory of Lyapunov functional and linear matrix inequalities. The controller gains are obtained by the matrix decoupling method. Finally, the feasibility and practicability of the method are verified by the circuit model and a numerical simulation.