Theory and Application on Adaptive-Robust Control of Euler-Lagrange Systems with Linearly Parametrizable Uncertainty Bound

TL;DR

This paper introduces an adaptive-robust control architecture for uncertain Euler-Lagrange systems with linearly parametrizable uncertainties, addressing limitations of conventional methods by avoiding overestimation and requiring no constant upper bound assumptions.

Contribution

It proposes the Adaptive Switching-gain based Robust Control (ASRC) that handles uncertainties without prior bounds and improves control performance over existing methods.

Findings

ASRC reduces overestimation and underestimation issues.

Experimental results show improved control with a wheeled mobile robot.

ASRC performs well with both linear and nonlinear uncertainties.

Abstract

This work proposes a new adaptive-robust control (ARC) architecture for a class of uncertain Euler-Lagrange (EL) systems where the upper bound of the uncertainty satisfies linear in parameters (LIP) structure. Conventional ARC strategies either require structural knowledge of the system or presume that the overall uncertainties or its time derivative are norm bounded by a constant. Due to unmodelled dynamics and modelling imperfection, true structural knowledge of the system is not always available. Further, for the class of systems under consideration, prior assumption regarding the uncertainties (or its time derivative) being upper bounded by a constant, puts a restriction on states beforehand. Conventional ARC laws invite overestimation-underestimation problem of switching gain. Towards this front, Adaptive Switching-gain based Robust Control (ASRC) is proposed which alleviates the overestimation-underestimation problem of switching gain. Moreover, ASRC avoids any presumption of constant upper bound on the overall uncertainties and can negotiate uncertainties regardless of being linear or nonlinear in parameters. Experimental results of ASRC using a wheeled mobile robot notes improved control performance in comparison to adaptive sliding mode control.