Optimal Control of Stochastic Markovian Jump Systems With Wiener and Poisson Noises: Two Reinforcement Learning Approaches

Abstract

This article investigates the infinite horizon optimal control problem for stochastic Markovian jump systems with Wiener and Poisson noises. First, a new policy iteration algorithm is designed by using integral reinforcement learning approach and subsystems transformation technique, which obtains the optimal solution without solving stochastic coupled algebraic Riccati equation (SCARE) directly. Second, through the transformation and substitution of the SCARE and feedback gain matrix, a policy iteration algorithm is devised to determine the optimal control strategy. This algorithm leverages only state trajectory information to obtain the optimal solution, and is updated in an unfixed form. Additionally, the algorithm remains unaffected by variations in Poisson jump intensity. Finally, an numerical example is given to verify the effectiveness and convergence of the proposed algorithms.