Neural Network-Based Sliding Mode Control for Semi-Markov Jumping Systems With Singular Perturbation

The primary focus of this article centers around the application of sliding mode control (SMC) to semi-Markov jumping systems, incorporating a dynamic event-triggered protocol (ETP) and singular perturbation. The underlying semi-Markov singularly perturbed systems (SMSPSs) exhibit mode switching behavior governed by a semi-Markov process, wherein the variation of this process is regulated by a deterministic switching signal. To simultaneously reduce the triggering rate and uphold the system performance, a novel parameter-based dynamic ETP is established. This protocol incorporates weight estimation of a radial basis function neural network (RBFNN) and introduces two internal dynamic variables. Following the Lyapunov’s theory, sufficient criteria are established for ensuring the mean-square exponential stability of the resulting system. Additionally, an SMC scheme based on the convergence factor is designed to fulfill reachability conditions. Finally, two examples are carried out to validate the solvability and applicability of the attained control methodology.