Adaptive-Robust Control of a Class of Uncertain Nonlinear Systems Utilizing Time-Delayed Input and Position Feedback

TL;DR

This paper introduces TARC, an adaptive-robust control method for uncertain nonlinear Euler-Lagrange systems that uses time-delayed input and position feedback to improve tracking accuracy without requiring prior uncertainty bounds.

Contribution

The paper proposes a novel adaptive-robust control strategy that estimates unknown dynamics via time delays and features a new adaptation law that avoids over/underestimation of gains.

Findings

Enhanced tracking accuracy demonstrated on a wheeled mobile robot

The control method does not require prior bounds on uncertainties

The approach effectively handles unknown dynamics with robustness

Abstract

In this paper, the tracking control problem of a class of Euler-Lagrange systems subjected to unknown uncertainties is addressed and an adaptive-robust control strategy, christened as Time-Delayed Adaptive Robust Control (TARC) is presented. The proposed control strategy approximates the unknown dynamics through time-delayed logic, and the switching logic provides robustness against the approximation error. The novel adaptation law for the switching gain, in contrast to the conventional adaptive-robust control methodologies, does not require either nominal modelling or predefined bounds of the uncertainties. Also, the proposed adaptive law circumvents the overestimation-underestimation problem of switching gain. The state derivatives in the proposed control law is estimated from past data of the state to alleviate the measurement error when state derivatives are not available directly. Moreover, a new stability notion for time-delayed control is proposed which in turn provides a selection criterion for controller gain and sampling interval. Experimental result of the proposed methodology using a nonholonomic wheeled mobile robot (WMR) is presented and improved tracking accuracy of the proposed control law is noted compared to time-delayed control and adaptive sliding mode control.