Linear Quadratic Optimal Control of Itô Stochastic Systems with Wiener and Poisson Noises

This paper investigates the infinite horizon optimal control problem for a class of continuous-time Itô stochasticˆ systems subject to continuous Wiener and discontinuous Poisson noises. Firstly, a stochastic algebraic Riccati equation (SARE) with Poisson jump intensity is provided for the concerned systems. Secondly, a numerical iterative algorithm is developed to converge the solution of the proposed SARE, and a new policy iterative algorithm, which depends only on the partial system dynamics, is designed by using the integral reinforcement learning method. In addition, a new algorithm is proposed to compute the maximum Poisson jump intensity under different the convergence accuracy of the proposed numerical and policy iterative algorithms. Finally, an actual example is given to illustrate the effectiveness and applicability of the proposed algorithms.