Fuzzy Adaptive Backstepping Control For Switched Pure-feedback Nonlinear Systems

Switched system,also known as a hybrid system,is composed of a series of subsystems and a dispatching subsystem signal.In a hybrid system,a switched system can be obtained by ignoring the details of discrete behavior and considering all possible switching modes from a certain class.The switching system lays more emphasis on the nature of continuous state,and the main problems are stability analysis and control synthesis.The research object of traditional automatic control theory is mainly linear systems,while most control objects in practical application are nonlinear systems,which contain many nonlinear phenomena,such as limit cycle,chaos and so on.How to overcome the adverse effects brought by nonlinear phenomena and construct an ingenious and appropriate control scheme has become the main research problems of nonlinear control theory.The control object of this paper is a switched pure feedback nonlinear system,and the stability problem of the system is studied mainly by combining Backstepping method,adaptive fuzzy control method and Lyapunov stability theory.The main contents are as follows:1)In this paper,the adaptive fuzzy theory is applied to a class of pure-feedback switched stochastic nonlinear systems.Firstly,a state observer is constructed,and a Butterworth low-pass filter is used to transform the non-affine form into affine.By using Lyapunov function method and Backstepping design method,an adaptive fuzzy output feedback tracking control scheme is proposed,and the actual controller is designed,and the system can stay stable under Lyapunov stability theory.The simulation result shows that the closed-loop signals are bounded and the tracking error converges to the neighborhood near the origin.2)For a class of pure feedback switched nonlinear systems with unknown gain,a switched state observer is constructed to estimate the unmeasured states in the system.Then,the Nussbaum function is used to deal with the problem of unknown gain,and the system is transformed into affine form by using the mean value theorem.By using several Lyapunov functions and Backstepping method,an adaptive fuzzy tracking control scheme under the switching signal of average dwell time is designed.The simulation result shows that the designed controller can guarantee the boundedness of all the signals in the closed-loop system under switched signals with average dwell time,and the output can follow the reference signal within a small region of error.