Stochastic Optimal Control of Quasi Integrable Hamiltonian Systems Subject to Actuator Saturation

A modified bounded optimal control strategy for quasi integrable Hamiltonian systems subject to actuator saturation is proposed. First, an n degree-of-freedom (DOF) weakly controlled quasi Hamiltonian system subject to Gaussian white noise excitation is formulated and converted into It equations by adding Wong-Zakai correction terms. Then, the averaged It stochastic differential equations and dynamical programming equation are derived by using stochastic averaging method and the stochastic dynamical programming principle, respectively. The optimal control law consisting of unbounded optimal control and bounded bang-bang control is obtained from solving the dynamical programming equation. Finally, an example of a two DOF controlled quasi integrable Hamiltonian system is worked out in detail. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with bang-bang control strategy.