Research On The Control Of Nonlinear Uncertain Systems With Time-delay Based On SOS

Nonlinearity, uncertainty and time-delay are ubiquitous and inevitable in practical systems. Therefore, the study of nonlinear uncertain systems with time-delay is of great importance. This thesis mainly concerns about a class of nonlinear uncertain systems with time-delay about some robust control problems. These problems include the guaranteed-cost stabilization via static output feedback, the non-fragile guaranteed-cost control and, the guaranteed-cost fault-tolerant control via state feedback. With the aid of polynomial sum of squares (SOS), the controller design for the aforementioned problems is converted into the SOS-based optimization problems. Thus the nonlinear controllers are derived from solving the related SOS-based optimization problems. The main contents of this paper are as follows:1) This thesis begins with the background and significance, followed by the research status in china and abroad.2) The theory of SOS and some important lemmas are introduced as the preliminaries for the later chapters.3) The problem of guaranteed-cost stabilization via static output feedback is studied. The guaranteed-cost stabilization controller is designed by using the static output feedback control strategy, Lyapunov stability theory, and SOS technique. It not only makes the closed-loop systems asymptotically stable for all possible uncertainties, but also satisfies certain quadratic performance index. The optimal guaranteed-cost stabilization controller via static output feedback and the minimum upper-bound of the quadratic performance index are obtained by solving the corresponding optimization problems.4) The fragility of the guaranteed-cost controller caused by the perturbations of the parameters in controller is studied. A non-fragile guaranteed-cost controller is designed with the aid of guaranteed-cost control strategy, Lyapunov stability theory, and SOS technique. It guarantees the asymptotic stability of the closed-loop system, while meets certain quadratic performance index. The optimal non-fragile guaranteed-cost controller and minimum upper-bound of the quadratic performance index are obtained by solving the corresponding optimization problems. 5) The problem of guaranteed-cost fault-tolerant control via state feedback is studied under the circumstance that the actuators partly fail. The controller and the optimal one are derived from the combination of the guaranteed-cost control strategy, Lyapunov stability theory, and SOS technique.