Study On Robust Adaptive Control For Switched Nonlinear Systems

With the continuous development of the social productive forces and the increasingly rise of requirement for control performance, the control problems of uncertain nonlinear switched systems have received a great deal of attention, and a great many of achievements have been reported. Switched system is represented by a switching logic organically subsystem collection. Many practical engineering systems themselves have the switching characteristics. In recent years the stability of switched system has become the hotspot of control theory, through the design of control input and switching rule to improve the performance of the switched system. At present, the methods using Common Control Lyapunov Function method (CCLF), Multiple Lyapunov Function method and Dwell-time method, play an important role. The main work is outlined as follows.Firstly, the problem of stabilization control is studied for a class of switched nonlinear systems in strict-feedback form in this paper. By introducing backstepping technique, and utilizing common control Lyapunov technique and Schur lemma, an improved switched control is developed. Compared with the existing literature, the proposed approach fully considers the virtual error term which is generated in backstepping design. The virtual error compensation term is adopted in controller. It is great convenient for stability analysis. By theoretical analysis, the closed-loop control system is shown to be globally uniformly asymptotically stable.Secondly, an adaptive neural network control scheme is proposed for a class of nonlinear switched systems in strict-feedback form. The design is based on the backstepping technique, the Lyapunov function of integral type, the approximation capability of neural networks, and the dwell-time approach. By introducing the adaptive compensation term of the approximation error, and utilizing Young’s inequality, the control performance of the closed-loop system is improved. Compared with the existing literature, the proposed approach relaxes the requirements of the system and eliminates the assumption that the amplitude of the state’s jump should be related to the tracking error. By theoretical analysis, the closed-loop control system is shown to be semi-globally uniformly ultimately bounded.Thirdly, an adaptive neural network control scheme is proposed for a class of nonlinear switched systems in pure-feedback form. The design is based on the dynamic surface technique, the approximation capability of neural networks and the dwell-time approach. The design makes the approach of dynamic surface control be extended to the nonlinear switched system, and relaxes the extent of application of the approach of dynamic surface control. Compared with the existing literature, the proposed approach relaxes the requirements of the system. And the explosion of complexity in traditional backstepping design caused by repeated differentiations of virtual control is avoided. By theoretical analysis, the closed-loop control system is shown to be semi-globally uniformly ultimately bounded.Lastly, an adaptive neural network control scheme is proposed for a class of nonlinear switched systems with unmodeled dynamics in pure-feedback form. The design is based on the dynamic surface technique, the approximation capability of neural networks and the dwell-time approach. The design makes the approach of dynamic surface control be extended to the nonlinear switched system with unmodeled dynamics, and relaxes the extent of application of the approach of dynamic surface control. Compared with the existing literature, the proposed approach relaxes the requirements of the system. And the explosion of complexity in traditional backstepping design caused by repeated differentiations of virtual control is avoided. By theoretical analysis, the closed-loop control system is shown to be semi-globally uniformly ultimately bounded.