Sampled-data robust practical tracking of Euler-Lagrange systems with an uncertain exosystem

This article focuses on the problem of sampled-data practical tracking for Euler-Lagrange systems subject to uncertain parameters. We assume that the system matrix of the exosystem and the Euler-Lagrange system both contain unknown parameters, which is clearly more practical. The existence of unknown system parameters invalidates existing control strategies and poses a major challenge to the solvability of the problem. With the help of the internal model principle and the adaptive control technology, we propose a novel sampled-data dynamic compensator to overcome the challenge of unknown parameters in exosystems. In particular, a virtual sampling adaptive control input is proposed to deal with uncertainties in the exosystem matrix. Then, a sampled-data control law is constructed to guarantee that, by any fast predefined rate, the tracking error exponentially approaches any small predefined ranges of the origin, thus ensure the tracking performance. Finally, we apply our result to a three-link robot manipulator system.