Adaptive Backstepping Control For A Class Of Single-Input Single-Output Nonlinear Systems

Nonlinear phenomenon often exists in the actual control systems.The adaptive control of nonlinear systems has become a hot research issue in control theory.The idea of adaptive control is to adjust the parameters and structure of controller automatically by using the state information or output information of the system,so as to overcome the influence of system uncertainty and achieve the desired control objectives.Backstepping technology is an important method to investigate nonlinear system control.The tracking error or system output signal converges to the origin with a small neighborhood by combing Lyapunov stability theory and adaptive backstepping control method.Based on the adaptive backstepping control technology,this paper will do some research for a class of single-input and single-output nonlinear systems as follows:In the second chapter,the adaptive stability control problem is studied for a class of strict-feedback nonlinear systems with unmodeled dynamics and unknown dead zone.Nussbaum gain technique is used to overcome the unknown control direction problem.The dynamic and assistant signals are constructed to dominate the unmodeled dynamics and compensate the influence of symmetric dead zone,respectively.In addition,nonlinear damping terms are framed to counteract the dynamic disturbances in strict-feedback nonlinear systems.Under the adaptive backstepping control framework and based on the Lyapunov stability theory,the proposed adaptive control scheme can guarantee the system performance.In the third chapter,when the direction of the controller is unknown,the adaptive tracking control problem is investigated for a class of single-input and single-output nonlinear systems with external disturbances in strict feedback form.The Nussbaum gain technique is employed to solve the unknown control direction problem.The dynamic surface control method is used to deal with the “explosion of complexity” problem that occurs in the traditional backstepping method.Novel controllers and adaptive laws are designed by combining the compensation tracking error and the prediction error that exist between the system state and the serial-parallel estimation model.In addition,by using Lyapunov stability theory,it is proved that all the variables in the closed-loop system are bounded and the tracking error is driven to the origin with a small neighborhood.In the fourth chapter,an adaptive event-triggered control problem is investigated for a class of stochastic nonlinear systems with full state constraints and actuator faults.A reduced-order observer is designed to observe the unavailable state variables.Fuzzy logic systems are adopted to approximate the unknown nonlinear functions.Barrier Lyapunov functions are constructed to guarantee that all the states of the single-input and single-output nonlinear system are not to violate their constraints.Combining the event triggering mechanism and the adaptive backstepping technique,an adaptive fuzzy output feedback control scheme is proposed to ensure that all the variables in the closed-loop system are semi-global practical finite-time stable.