Adaptive Fault-Tolerant Reachable Set Synthesis for Nonlinear Singular Hidden Semi-Markov Jump Systems Via Event-Triggered Approach

The problem of reachable set synthesis (RSS) for nonlinear singular hidden semi-Markov jump systems (NSHSMJSs) with bounded disturbances is studied. Firstly, to solve the problem of limited communication resources in networked systems, the event-triggered approach (ETA) is utilized. The introduction of ETA inevitably leads to asynchronous behavior between the controllers and the systems. To address the asynchronous behavior between the systems and controllers, the hidden Markov model is adopted. In addition, to eliminate the impact of actuator failures and denial-of-service attacks on system performance, an adaptive security fault-tolerant asynchronous controller is designed. Subsequently, we apply Lyapunov stability theory to derive sufficient conditions for the RSS of NSHSMJSs. Then, the matrix transformation technique is used to obtain the gains and weighting matrices. Finally, the effectiveness and feasibility of the theoretical results proposed in this paper are verified through two examples.