A stochastically averaged optimal control strategy for quasi-Hamiltonian systems with actuator saturation

A stochastic optimal control strategy for quasi-Hamiltonian systems with actuator saturation is proposed based on the stochastic averaging method and stochastic dynamical programming principle. First, the partially completed averaged Itô stochastic differential equations for the energy processes of individual degree of freedom are derived by using the stochastic averaging method for quasi-Hamiltonian systems. Then, the dynamical programming equation is established by applying the stochastic dynamical programming principle to the partially completed averaged Itô equations with a performance index. The saturated optimal control consisting of unbounded optimal control and bounded bang–bang control is determined by solving the dynamical programming equation. Numerical results show that the proposed control strategy significantly improves the control efficiency and chattering attenuation of the corresponding bang–bang control.