Adaptive-Robust Control of Uncertain Euler-Lagrange Systems with Past Data: A Time-Delayed Approach

A new adaptive robust control strategy, christened as Adaptive Time-delayed Robust Control (ATRC) is presented in this paper for trajectory tracking control of a class of Euler-Lagrange systems subjected to uncertainties with unknown bounds. The adaptive law to compute the switching gain of the conventional adaptive-robust controllers require either complete nominal modelling of the system or uncertainty bound. The proposed control framework amalgamates the best features of the switching control logic and time-delayed logic. The proposed control strategy approximates the unknown dynamics through time-delayed logic, and the switching logic provides robustness against the approximation error. A novel adaptive law for the switching control is developed which does not require uncertainty modelling or the knowledge of its bound and the switching gain adapts itself according to the tracking error incurred by the system. Moreover, a new design methodology and stability criterion for time-delayed control is proposed. Experimental results 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 the conventional time-delayed control and time-delayed control with gradient estimator.