Trajectory Tracking Control of Euler-Lagrange Systems with ISS-Like Robustness to Actuator Noises

This paper studies global robust tracking of uncertain Euler-Lagrange systems with input disturbances. The authors develop a robust regulation-based approach for the problem. Specifically, by introducing a novel nonlinear internal model, the authors solve global asymptotic trajectory tracking with disturbance rejection of multiple step/sinusoidal signals with unknown amplitudes, frequencies, and phases. Moreover, the authors show that a robustness property to actuator noises can be guaranteed in a sense of strong integral input-to-state stability (iISS). That is, the closed-loop system is not only iISS but also input-to-state stable (ISS) to small magnitude actuator noises. Furthermore, the authors explore a by-product overparametrized linear regression estimation, coming up with robust estimation of the unknown parameters. Finally, the authors present several numerical examples to illustrate the theoretical results.