A New Design Methodology of Adaptive Sliding Mode Control for a Class of Nonlinear Systems with State Dependent Uncertainty Bound

In this paper, a new Adaptive Sliding Mode Control (ASMC) framework is proposed for the tracking control of a class of uncertain nonlinear systems where system states are present explicitly in the upper bound of the overall (or lumped) system uncertainty. Conventional ASMC strategies presume that either the overall (or lumped) uncertainty of the system or its time derivative is norm bounded by a constant. However, such assumption restricts the evaluation of the states a priori for the class of systems that has been considered in this paper. The proposed ASMC law does not presume such constant upper bound on the system uncertainties and, rather, exploits the unique structure of the uncertainty bound to design the control law. Moreover, the adaptive law of the proposed ASMC alleviates the overestimation-underestimation problems of switching gain which is commonly observed in the existing ASMC laws. Simulation results using a two-link manipulator demonstrate improved control performance of the proposed controller in comparison to the conventional ASMC.