A nonlinear stochastic optimal bounded control using stochastic maximum principle

A nonlinear stochastic optimal bounded control strategy for quasi-Hamiltonian systems with actuator saturation is proposed based on the stochastic averaging method and stochastic maximum principle. First, the averaged Itô stochastic differential equations are derived by using the stochastic averaging method for quasi-Hamiltonian systems. Then, the stochastic Hamiltonian system for optimal control with a given performance index is established based on the stochastic maximum principle. The bounded optimal control consisting of unbounded optimal control and bounded bang–bang control is determined by solving the forward-backward stochastic differential equations with control constraint. Finally, three examples of quasi-Hamiltonian systems with controls are given to illustrate the application of the proposed strategy. Numerical results show that the proposed control strategy significantly improves the control efficiency and chattering attenuation of the corresponding bang–bang control.