Self-Triggered Optimal Control for Unknown Nonlinear Random Power Systems With Markovian Switching

This article explores the challenge of triggered optimal control for random differential equations (RDEs) with Markovian switching. We initially address the inherent contradiction between whether to comply with or bypass the event-triggered mechanism. By navigating this challenge, we ensure noise-to-state stability (NSS) for RDEs through event-triggered control (ETC). Furthermore, we establish that random nonlinear systems utilizing self-triggered control (STC) can achieve NSS, by setting a minimum triggering time to prevent Zeno behavior. Lastly, by adopting the adaptive dynamic programming (ADP) strategy, we develop self-triggered optimal control for random systems with Markovian switching, ensuring the uniform ultimate boundedness (UUB) of the signals in all closed-loop systems. This article addresses three key gaps in the field of RDE optimal control, contributing substantially to both theoretical and practical advancements. To demonstrate the method’s feasibility, we include a representative example with simulation results.