Constrained Output Regulation For A Class Of Nonlinear Systems Based On Barrier Lyapunov Function

Adaptive output regulation has always been a very important research topic in the field of control theory.The objective of this study is to design an output feedback controller to enable the system output track the given reference signal asymptotically while satisfying the stability of the closed-loop system.Traditional quadratic Lyapunov function technique can handle the problem of adaptive output regulation very well,but it cannot guarantee the transient performance of the system.Time-varying barrier Lyapunov function is a new technique to construct Lyapunov function with system output tracking error and time-varying error constraint function,which can effectively solve the output regulation problem of nonlinear system with output constraint.The actual physical systems are usually nonlinear systems with unknown partial structures in daily engineering applications.When adjusting the output of such systems,the control direction is often difficult to determine.Moreover,the output of many systems is limited by the external environment.Considering the above factors,in this paper,by combining barrier Lyapunov function and Nussbaum gain technique,an output feedback controller is designed to solve the output regulation problem of nonlinear systems with output constraint and unknown control direction.The contents of this study can be summarized as follows:1.The problem of adaptive output regulation of nonlinear system with output constraint is solved.Firstly,according to the principle of internal model,an appropriate internal model of the system is designed,and coordinate transformation is carried out to transform the output regulation problem of the original system with output constraint into the adaptive stability problem of the augmented system in the case of limited state.Then,combining barrier Lyapunov function and adaptive control technology,an appropriate output feedback controller is designed to deal with the adaptive stability problem of the augmented system,and then the output regulation problem of the original system is solved.Finally,Lorenz system is selected for simulation to verify the effectiveness of the controller.2.On the basis of solving the output limitation problem of nonlinear system,the unknown control direction of the system is further discussed.Based on the general theoretical framework of solving output regulation problem,a feedback controller is designed by combining barrier Lyapunov function and Nussbaum-type function to solve the output regulation problem of a class of nonlinear systems with output constraint and unknown control direction.Moreover,based on MATLAB simulation,the effectiveness of the control algorithm is verified.3.The logarithmic barrier Lyapunov function is improved to be applicable to the output regulation problem of nonlinear systems with and without state constraints.Then,the improved barrier Lyapunov function is used to design the output feedback controller,which solves the output regulation problem of the nonlinear system with state constraints.Finally,the effectiveness of the controller is verified by numerical simulation.