Practical tracking control with prescribed transient performance for Euler-Lagrange equation

Abstract

This paper is devoted to the practical tracking control with prescribed transient performance for a class of uncertain Euler-Lagrange (EL) equations. Remarkably, the system allows serious nonparametric uncertainties since all the system matrices are unknown and do not necessarily have known bounds. Moreover, the reference trajectory to be followed is more general since it does not necessarily have known bound or require to be twice-continuously differentiable but those of literature must do. For this, a funnel-based control scheme is proposed to overcome the serious uncertainties, and in turn to achieve certain prescribed closed-loop performance. Specifically, a funnel to which the tracking error belongs is first skillfully constructed with the aid of a time-varying function about a prescribed tracking accuracy parameter. Based on the funnel, a time-varying controller is designed which guarantees that all the closed-loop system signals are bounded while the tracking error evolves in the funnel set, that is, the system output tracks the reference trajectory with the prescribed convergence rate before the prescribed time. Finally, two application examples are used to validate the effectiveness of the theoretical results.