Study On Several Problems In Nonlinear Stochastic Optimal Control Of Quasi-Hamiltonian Systems

There are some unavoidable problems in practical application of the feedback control theory, such as partial observation of the system state, time-delay in the feedback control forces, semi-active characteristics of the control actuators and uncertainty of system parameters. In the present dissertation, the nonlinear stochastic optimal control considering these problems is investigated in the framework of nonlinear stochastic optimal control theory of quasi-Hamiltonian systems.In chapter 1, a brief review of the development of control theory is presented, with a special introduction of the framework of nonlinear stochastic optimal control theory of quasi-Hamiltonian systems developed by Zhu and his group. After introducing the three problems, i.e., partial observation, time-delay and semi-active problem, the objective, as well as the theoretical significance and practical value of the following work presented in this dissertation is pointed out.The problem of parametric uncertainty and related robustness analysis technique are present in chapter 2, where a new statistical model calledλ-PDF distribution is introduced, a probabilistic robustness analysis technique using sensitivity of variation coefficients is given and then used to evaluate the robustness of a feedback stabilizing control strategy for quasi-non-integrable Hamiltonian systems.Chapter 3 is devoted to the stochastic optimal control problem of partially observable nonlinear systems, which is generally difficult to tackle since it consists of coupled filtering and control problems. With the help of a theorem proved by Charalambous and Elliott, the original problem is recast into a completely observable linear control problem of finite dimension. For the system without parametric uncertainty, the problem is then solved by using the nonlinear stochastic optimal control strategy based on stochastic averaging method and stochastic dynamic programming, while for the system with parametric uncertainty, the minimax stochastic optimal control strategy based on stochastic averaging method and stochastic differential games is adopted. In chapter 4. the stochastic optimal time-delay control problem is investigated. The time-delay is induced by the time spent in the measurement of system state, filtering and data processing, calculating and executing the control force, etc. Only the time-delay in the feedback control is considered in the present dissertation. The method developed here is based on an approximation concerning time-delayed state of the quasi-integrable Hamiltonian systems proposed by Liu and Zhu. For the case of system with parametric uncertainty, the time-delay control strategy is proposed by combing the nonlinear stochastic optimal control strategy and then used to a two degree-of-freedom example. For the case of system without parametric uncertainty, the corresponding time-delay control strategy is proposed by combing the minimax stochastic optimal control strategy.The stochastic optimal time-delay control problem by using actuators (MR dampers) is investigated in chapter 5. Also both the cases of systems with and without parametric uncertainty are considered. By the similar procedure for stochastic optimal time-delay control developed in the previous chapter, the stochastic optimal time-delay semi-active control strategies for both cases are proposed. It is showed that the proposed stochastic optimal time-delay control method has the capability to depress or avoid the possible performance deteriorating or even destabilizing effects caused by time-delay.Finally, in chapter 6 the work present in this dissertation is concluded and several possible promising directions of future research are pointed out.