Research On Finite-time Control For Some Nonlinear Systems

The study of controlling nonlinear systems has received considerable attention due to its broad applications in different fields. With the fast development of science and technology, it requires a further understanding of the dynamical behaviors of nonlinear dynamical systems. The concept of finite-time stability arises naturally in time optimal control. Compared to the conventionally asymptotic stability control, finite-time convergence usually demonstrates faster convergence rates, higher accuracies, better disturbance rejection properties, and robustness against uncertainties. In recently years, finite-time control for nonlinear systems has been hot topics and received much attention from all over the world. Research on those topics is not only of great theoretical values but also of practice signification. Based on the finite-time Lyapunov method, homogeneous theory, matrix inequality as well as control theory, this dissertation addresses finite-time control for some nonlinear systems. This dissertation is divided into six chapters and the organization is as follows.In the first chapter, the significance and the development tendency of control for nonlinear system and finite-time control together with current research situation are briefed. The main contents and the main contributions of this dissertation are also expounded according to the above-mentioned analysis.In the second chapter, finite-time synchronization and finite-time lag synchronization of hybrid coupled networks are investigated. There is only one transmittal delay in the delayed coupling. Because the time delay affects the variable when the information from one system to another in the signal transmission process, so assume that there is only one single time-varying delay coupling is more consistent with the reality. At the same time, the internal delay and coupling delay are time-varying and different. Based on the finite-time Lyapunov stability theory, several sufficient conditions are derived by means of state feedback control to ensure two coupled networks to be synchronization or lag synchronization in finite time. Numerical simulations are presented to demonstrate the effectiveness of the theoretical results.In the third chapter, the problem of finite-time synchronization between two high-order nonlinear systems with parameter uncertainties is considered. When all of the states infor-mation are available, we propose a state feedback controller to achieve the synchronization in finite time. An observer-based output feedback controller is adopted to guarantee the conver-gence of the slave system trajectories to the trajectories of the master system in finite time if only the information relative outputs can be obtained. Finally, simulation examples are given to illustrate the theoretical analysis.The forth chapter elaborates on investigating the finite-time stabilisation for a class of lower-triangular high-order systems. Based on state transformation and finite-time Lyapunov theory, a state feedback controller with a dynamic gain is derived. Moreover, using the ho-mogeneous domination approach, we scale the finite-time convergent observer for the systems only the information relative outputs can be obtained. Compared with some existing results, the designed controllers have a very simple structure which can be easily implemented.The fifth chapter discusses the finite-time stability of chaotic systems. A new model based on Takagi-Sugeno fuzzy model is proposed for representing chaotic systems with time-varying delay and parameter uncertainties. Sufficient conditions are given in terms of matrix inequalities, which guarantees the finite-time stability can be achieved.In the sixth chapter, the research work of this dissertation is summarized. Furthermore, the possible improved methods are proposed and the prospect for the future work is made.