Design of output feedback tacking controllers for Euler-Lagrange systems by using a Lyapunov function-based procedure

A procedure to design output feedback tracking controllers for Euler-Lagrange systems is proposed. This procedure is based on the natural energy Lyapunov function, unifying the stability analysis for designs of control laws in the situations of either unconstrained or constrained torque input. Since only generalized positions are measured, dynamic filtering is used to obtain an estimation of the velocity tracking error. In the stability analysis we show the global exponential convergence result for the position and velocity tracking errors, and the local exponential convergence result for the output of the dynamic filtering.

I. Introduction

By invoking Krasovskii—LaSalle's theorem, Takegaki and Arimoto [1] considered an energy Lyapunov function consisting of the total kinetic energy and a desired potential function to generate a class of position regulators. This procedure received after several extensions and improvements, specially for the tracking control problem, see e.g., [2], [3], [4]. In the work of Santibáñez and Kelly [5] is presented an interesting historical review as well as theoretical justifications of the natural Lyapunov function—based approach to design full state regulators and tracking controllers for robot manipulators.