Robustness Of Nonlinear Stochastic Optimal Control And Robust Control For Uncertain Quasi Hamiltonian Systems

The present dissertation consists of two parts. In the first part, the robustness of the nonlinear stochastic optimal control for uncertain quasi Hamiltonian systems is studied. Based on the independence of uncertain parameters and stochastic excitations, the nonlinear stochastic optimal control for the nominal quasi Hamiltonian system with average-value parameters is firstly obtained by using the stochastic averaging method and stochastic dynamical programming principle. Then, the means and standard deviations of root-mean-square responses, control effectiveness and control efficiency for the uncertain quasi Hamiltonian system are calculated by using the stochastic averaging method and the probabilistic analysis. By introducing the sensitivities of the variation coefficients of controlled root-mean-square responses, control effectiveness and control efficiency to those of the uncertain parameters as measures, the robustness of the nonlinear stochastic optimal control is evaluated. As the application of the nonlinear stochastic optimal control strategy, controlled Bouc-Wen and Preisach hysteretic systems are studied and the robustness of the control strategy is also analyzed. Numerical results show the remarkable robustness of nonlinear stochastic optimal control.In the second part, the robust control of uncertain quasi Hamiltonian systems is studied. A minimax optimal control strategy for quasi Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. The proposed strategy is searching for the optimal worst-case controller by solving a stochastic differential game problem, and the worst-case disturbances and the corresponding optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs equation. The feedback stabilization of uncertain quasi Hamiltonian systems are investigated as a generalization of the above robust control strategy. The form of the worst-case disturbances and the optimal controls are firstly obtained by solving a stochastic differential game problem with undetermined cost function. The cost function is then determined by the requirement of minimizing the maximal Lyapunov exponent of the controlled system in worst case.