Actor-Critic Optimal Control for Semi-Markovian Jump Systems With Time Delay

In this brief, an actor-critic neural network (NN) framework is constructed to address the optimal regulation problem of the nonlinear semi-Markovian jump systems with state and input delays. Firstly, a specialized cost function associated with semi-Markovian jump parameters (s-MJPs) is defined. Then, the resolution of the Hamilton-Jacobian-Bellman equation is ascertained based on the application of actor-critic NN, in which updating laws for both the actor and critic NNs are devised to concomitantly execute the reinforcement learning strategy. Wherein the temporal difference error takes into account state and input delays. An actor-critic NN scheme is designed to approximate the unknown dynamic for time-delay systems with s-MJPs. Utilizing the Lyapunov method, this brief successfully demonstrates the ultimate uniform boundedness of the considered system. Finally, the practical simulation results presented serve to validate the efficacy of the proposed algorithm.