Stochastic optimal control of MDOF quasi non-integrable Hamiltonian systems with actuator saturation

摘要

A new bounded optimal control strategy for multi-degree-of-freedom (MDOF) quasi non-integrable Hamiltonian system with actuator saturation combining both advantages of unbounded and bang-bang control strategies is proposed. First, an n DOF controlled quasi non-integrable Hamiltonian system is reduced to a partially averaged It? stochastic differential equation by using stochastic averaging method for quasi non-integrable Hamiltonian systems. Then, a dynamical programming equation is established by using stochastic dynamical programming principle, from which the control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted from solving the Fokker-Planck-Kolmogorov (FPK) equation associated with fully averaged It? equations. An example of a two DOF controlled quasi non-integrable Hamiltonian system is worked out in detail. Numerical results show that the proposed strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with bang-bang strategy.