Adaptive sliding mode control of a class of nonlinear systems with artificial delay

In this paper, an adaptive-robust control (ARC) strategy, christened as Adaptive Time-delayed Sliding Mode Control (ATSMC) is presented for trajectory tracking control of a class of uncertain Euler-Lagrange systems. The proposed control framework brings together the best features of the switching control logic and time-delayed logic. ATSMC uses artificial time delay to approximate the unknown dynamics through time-delayed logic, and the switching logic provides robustness against the approximation error. The adaptation law for the switching gain of the conventional ARC methodologies suffer from over- and under-estimation problems. The novel adaptive law of ATSMC alleviates the over- and under-estimation problems of switching gain. Moreover, a new design methodology and stability criterion for time-delayed control is proposed which provides an upper bound on the allowable delay time. 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 time-delayed control and conventional adaptive sliding mode control.