Finite-time Controller Design And Analysis Via Output Feedback For Stochastic Nonlinear Systems

Since stochastic models are widely applied in the finance and engineering fields, the control the-ories of stochastic systems have received much attention. In many engineering fields, it is desirable that the trajectories of a dynamical system converge to its equilibrium in finite time. Finite-time stability enjoys not only faster convergence, but also better robustness and anti-interference ability. When the system states are not measured or available, it is meaningful and challenging work to design the output-feedback stabilization controller via estimating the states by the output. Inverse optimal control is also known as zero-sum differential game, and is closely related to the optimal control problem of risk sensitivity index. Its specific meaningful cost functional includes penalty on state and control effort, which has an infinite gain margin and therefore it could have higher practical value and better performance.In this thesis, for several classes of stochastic nonlinear systems, we consider the design of finite-time output-feedback stabilization controllers and finite-time inverse optimal control problem. The main work includes:(1) For a class of non-smooth stochastic nonlinear systems, the design method of finite-time output-feedback stabilization controller is given. Firstly, under the condition that the state variables are measurable, we design a finite-time state-feedback controller; Then, we design a new observer with gains to be determined; Finally, we determine the observer gains step by step to guarantee that the closed-loop system is globally finite-time stable in probability. A numerical simulation example is given to illustrate the effectiveness of the controller.(2) A finite-time inverse optimal output-feedback controller is designed for the system in (1). According to the concept of stochastic finite-time control Lyapunov function, and based on the fundamental theory of using stochastic control Lyapunov function to construct the optimal controller about specific meaningful cost functional, we give the design of the inverse optimal controller under the meaning of stochastic finite-time stability, and design the finite-time inverse optimal output-feedback controller for the system in (1).(3) For a class of high-order stochastic nonlinear systems with uncertain parameters, finite-time output-feedback stabilization controller is designed. First we design a dynamic output-feedback controller for the corresponding nominal system without the nonlinearities and stochastic pertur-bations. Then a new observer is constructed and the gains of the observer are designed such that the closed-loop system is globally finite-time stable in probability. A numerical simulation example is given to illustrate the effectiveness of the design method.