  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.
