Robust Control Theory And Its Application On Nonlinear Systems

Although much attention has been paid to the nonlinear H∞ control and many important achievements have been obtained in recent years, lots of work are still to be done. The relevant nonlinear H∞ control theories need to be improved, while the existing results should be applied urgently.In this dissertation, the basic theoretic results on nonlinear H∞ control theory are summarized and developed firstly from the perspective of dissipation theory, then the robust H∞ control problems of uncertain nonlinear systems, especially those of the nonlinear systems with multiple time delays, and several other problems related to the H∞ control are investigated based on the theoretic results above. The contributions of this dissertation are as follows.1. The robust H∞ control problems of nonlinear systems with state perturbations are studied. The corresponding sufficient conditions for the solvability of H∞ control problems via the state feedback control, the output control and the output control based on observers are put forward, while the design methods of these kind controller are proposed. Then the performance criteria design is discussed for a class of nonlinear uncertain systems with state perturbations and state's derivative perturbations as well.2. Robust disturbance attenuation problems for uncertain upper-bounded nonlinear systems with multiple time delays are solved. The design methods via the state feedback control and the output control are put forward. Particularly, an output feedback controller is constructed by using the LMI method and the matrices related to the controller are parameterized. Combining H∞ control theory and adaptive control theory, I designed adaptive controllers for robust stabilization and robust disturbance attenuation of uncertain nonlinear systems with multiple time delays whose upper bounds are partially known are designed.3. The H∞ control theories are applied to solve model reduction problems, output tracking problems and filtering problems. The H∞ model reduction problem of akind of uncertain nonlinear systems with multiple time delays is studied. Model reduction methods are presented that can simplify the uncertain nonlinear systems with multiple time delays to be low order linear delayed systems or low order linear systems, or even the zero order input-output mappings. The output tracking problem of disturbed nonlinear systems is solved by the H∞ control theory, the analysis method is proposed. The sufficient conditions for the solvability of the H∞ filtering problem of nonlinear systems are obtained.4. The mixed H2/H∞ control problem of nonlinear systems is investigated. The relationships among the H∞ control, the H∞ control and the mixed H∞/H∞ control are explained. A unified formula for the H∞ control, the H∞ control and the mixed H∞/H∞ control is deduced.5. The nonlinear H∞ and H2/H∞ control theories are applied to solve the problem of robust H∞ control and the problem of disturbance almost decoupling of the rigid body attitude systems and the robot systems to verify the rationality and the validity of the results proposed in this dissertation.