Adaptive Robust Control For Uncertain Nonlinear Systems And Its Application

Adaptive robust control for uncertain nonlinear systems and its application in spacecraft attitude control systems are investigated in this thesis.First, geometric basis of nonlinear control is introduced. The basic mathematical concepts: differential manifolds, vector fields, Lie derivatives and distributions are explained successively, which are the foundation for developing the differential geometric control theory of nonlinear control systems.Second, robust linearization problem of nonlinear systems is developed. For affine nonlinear systems, the necessary and sufficient condition for exact linearization of the systems is presented; When uncertainties are considered, the expressions of matching condition and extended matching condition in differential geometry are given; In order to solve the control problem of nonlinear systems with uncertainties, the concept of linearizable nonlinear system set is suggested, i.e., the concept of robust linearization is presented.Thirdly, based on the robust linearization of nonlinear systems given above, the design problem of robust stabilization controllers for nonlinear systems is developed systematically. According to canonical form of nonlinear systems, the zero dynamics is introduced, which is used to obtain the sufficient condition for asymptotical stabilization of certain nonlinear systems; Then the robust stabilization control problem of uncertain nonlinear systems is investigated. As the bounded disturbance exists in nonlinear systems, a robust δ- stabilizable controller design is presented. For the systems with time invariant uncertainties, the invariant robust δ-stabilizable controller is designed under matching condition and unmatching condition, and the adaptive robust stabilization controllers are designed for three cases: matching condition case, extended matching condition case and unmatching condition case. For the system with time varying uncertainties, a robust stabilization controller design is also given, which has recursive form.Finally, by using the theoretical contributions presented in this thesis, the robust stabilization design problem for spacecraft attitude control systems is investigated. An adaptive controller for partial state robust stabilization of spacecraft attitude control systems is given. The simulation results show that the theoretical contributions here are correct.