Adaptive singularity-free controller design of constrained nonlinear systems with prescribed performance

Abstract

This paper investigates the controller design for the tracking problem of uncertain nonlinear systems with constraints on input and output. First, to avoid the full-state measurement, the high-gain observer is designed to estimate the unmeasured state. Compared to existing observer design for nonlinear systems, the high-gain observer design only requires a modified version of the Lipschitz condition. The output feedback controller is further presented on this basis. Second, to consider the transient constraints on the tracking performance, a barrier Lyapunov function with the user-defined time-varying performance is developed. In addition, the proposed controller design is shown to be free of control direction singularity. The convergence of the learning scheme and the boundedness of all the closed-loop signals during the learning phase are discussed theoretically. Finally, two simulation examples are conducted to verify the advantage of the proposed adaptive output feedback controller design.