The Nonlinear Stochastic Optimal Control Of Quasi Hamiltonian Systems With Actuator Saturation

The stochastic optimal control for minimizing the response of quasi Hamiltonian systems with actuator saturation is investigated. For multi-degree-of-freedom quasi non-integrable and integrable Hamiltonian systems with actuator saturation, the partially averaged It(o|^) stochastic differential equations are first obtained by using the stochastic averaging method, then the dynamical equation is established by using the stochastic dynamical programming principle, and finally the optimal bounded control law is obtained by solving the dynamical equation. In the case of partially observable nonlinear systems with actuator saturation, the partially observable control problem is first converted into completely observable control problem of linear system of finite dimension by using Charalambous and Elliott theorem. The optimal control law is then obtained by using stochastic averaging method and stochastic dynamical principle. For hysteretic system with actuator saturation, the hysteretic force is represented by using Bouc-Wen model and split into nonlinear elastic restoring force and nonlinear damping force. Then, the original hysteretic system is replaced by a equivalent nonlinear non-hysteretic system. Finally, the optimal control law for hysteretic systems is obtained by using stochastic averaging method and stochastic dynamical principle. For each case, the probability and statistics of the response of uncontrolled and controlled systems are obtained via solving the Fokker-Planck-Kolmogorov equation. Theoretical results are configured by using the results from Monte Carlo simulation and both the two results show that the proposed optimal control strategies are very effective and efficient.