Observer-based Adaptive Backstepping Control For Nonlinear Systems

Fuzzy logic systems and neural networks have powerful approximation ability in solving control problems of highly nonlinear and seriously uncertain systems.Adaptive fuzzy /neural networks control are based on the fundamental principle of adaptive method.It is designed by using the characteristics and theory of fuzzy logic systems/neural networks,which provides a new method for the study of nonlinear control.On the other hand,adaptive control of nonlinear systems can be roughly divided into state feedback control and output feedback control.State feedback control is suitable for the case in which all the systems states are known or measurable.Considering the fact that most state information is difficult to obtain in practical applications,thus an observer is natural to be used to estimate these immeasurable states.In addition,there are also various nonlinear phenomenons in actual systems.These nonlinearities,saturation,constraints,faults and so on,which often lead to the degradation of system performance or even destroy the stability of the system.This paper studies the observer-based adaptive control in the context of several kinds of nonlinear systems with immeasurable states by using the backstepping technique and Lyapunov stability theory,and the organization of the paper is given as follows:The Nussbuam function is introduced to compensate the nonlinearities included in a saturation function;the barrier Lyapunov function is used to guarantee that the system output remains in a pre-set bound;an intermediate signal is applied to obtain the controller based on the triggering event and actuator failure modes.The controllers are designed by combining adaptive fuzzy/neural method and Lyapunov stability theory.Finally,some simulation examples are used to testify the effectiveness of the proposed results.