Neuro-Control for Continuous-Time Stochastic Nonlinear Systems via Online Policy Iteration Algorithm - Zhou, Tianmin; Hou, Jiaxu; Li, Handong; Di, Zengru; Zhao, Bo (Chinese Control and Decision Conference, 2020)
This paper is concerned with the neuro-control for continuous-time nonlinear systems subject to stochastic disturbance. Due to the stochastic disturbance, the traditional value function in existing literature cannot meet the stochastic control problems, since mixed second partial derivatives are employed to construct modified value function of conditional expectation. To solve the Hamilton-Jacobi-Bellman equation, a novel online policy iteration algorithm with an Ito correction term is developed with establishing a critic neural network to approximate the optimal value function.ˆ Thus, the online optimal control can be obtained in a closed-loop form. The closed-loop system is guaranteed to be stable in probability via Lyapunov's direct method. Finally, numerical example is provided to illustrate the effectiveness of the developed control method.