Optimal Control for A Class of Linear Stochastic Impulsive Systems with Partially Unknown Information

This paper studies the optimal impulsive control problems of linear stochastic impulsive systems with periodic impulses and partially unknown information. By utilizing the collocation method combined with a periodic Lyapunov function, a sufficient condition for stochastic optimal impulsive control is derived in terms of a hybrid Riccati equation. Based on Bellman’s dynamic programming principle, an online reinforcement learning algorithm is further presented to attain optimal impulsive control with partial system information. A numerical simulation illustrates the effectiveness of the proposed control method.