Robust Control Of Stochastic Nonlinear Systems In Presence Of Dynamic Uncertainties

From the viewpoint of stochastic dissipation, the H∞control problems for the stochastic nonlinear systems in presence of dynamic uncertainties are studied. Especially, for the input dynamic uncertain stochastic nonlinear systems, the theory of stibalization is developed based on the conception of robust passivity and the L2 -gain design problems are resolved from the dissipation point of view.The research work of this dissertation is as the follows:1. From the view of stochastic dissipation, the L2 -gain performance design of stochastic nonlinear systems with dynamic uncertainties is investigated. Under some mild assumptions on the unmodeled dynamics, the relationship between the L2 -gain of this kind of stochastic systems and the solution to a certain HJI inequality is established. Furthermore, for some systems satisfying some proper matching conditions, the methods of acquiring the control laws without solving HJI inequality are discussed.2. From the viewpoint of passivity, robust control theory was developed for a class of stochastic nonlinear systems with input dynamic uncertainties. In particular, the passive-based systematic design approach associated with deterministic nonlinear systems is introduced for this type of uncertain stochastic systems, and is used to address the robust control design problems. Different from the classical design approach focused on triangular systems, the control law can be constructed for general systems which are not restricted to strict-feedback systems. The design procedure mainly contains two parts. Firstly, a stochastic passivity condition is presented for a stochastic non-linear system in feedback interconnection form, and after some proper assumptions and analysis, a state feedback control law is designed under this condition for a type of stochastic nonlinear systems in presence of input dynamic uncertainties. Then, the passivity control law is extended to the stochastic non-linear system with both static model uncertainties and dynamic uncertainties. Simulation results illustrate its effectiveness.3. From the view of stochastic dissipation, the robust H∞control problem for a class of stochastic non-linear systems with uncertain input dynamics is investigated. Through constructing the state feedback control laws to render the uncertain systems stochasticγdissipated, we address the L2 -gain design problems for the uncertain stochastic nonlinear systems under two assumptions -- systems satisfying some proper matching conditions and systems not satisfying these matching conditions. Furthermore, in the same way, the control laws of the stochastic non-linear systems with both dynamic and static model uncertainties are designed. Then, two examples are given to demonstrate the proposed approach.4. The theory of robust H∞control for a class of stochastic non-linear systems with uncertain input dynamics and unknown covariance is developed from the view of stochastic dissipation. By introducing the notion of stochastic dissipation for this kind of systems, we point out that theγstochastic dissipative system has the L2 -gain property. Through constructing the state feedback control laws to render the uncertain systems stochasticγdissipated, we address the H∞control problems for the uncertain stochastic nonlinear systems of unknown covariance under two assumptions—systems satisfying some proper matching conditions and systems not satisfying these matching conditions. Furthermore, in the same way, the control laws are designed for a type of stochastic non-linear systems driven by noise of unknown covariance, in presence of both dynamic and static model uncertainties.