Optimal Control of Discrete-Time Stochastic Systems with Wiener and Poisson Noises: A Model-Free Reinforcement Learning Approach

This paper investigates the problem of optimal control of discrete stochastic Poisson systems. First, the discrete stochastic algebraic Riccati equation containing Poisson noises is proved, and a model-based iterative method is proposed to solve it. Second, by using the system reconstruction method, a model-free reinforcement learning algorithm is presented, which operates without necessitating system matrixs and relies solely on the state trajectory information to derive the optimal solution. Third, it demonstrates that the incorporation of exploration noises does not impact the results of the algorithm. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.