Adaptive sliding mode control for a class of mismatched uncertain systems

This paper is concerned with an adaptive Sliding Mode Control (SMC) for a class of mismatched uncertain systems. The dynamic system to be considered here is described by a non-linear state equation subject to an uncertain disturbance and the state is measured in the contamination with random noise. The mismatched uncertainties are parameterised linearly in the unknown constant parameter terms, and the estimates for the state and the uncertainties are respectively taken by using the Sliding Mode Observer (SMO) and the Weighted Least Squares Estimator (WLSE). The proposed adaptive SMC is constructed by the information of the estimates for the state and uncertainties. It is verified by using the Lyapunov method that the estimation errors converge to zero as time increases and the dynamic system is ultimately stable on the sliding surface under the action of the proposed adaptive SMC. The effectiveness of the proposed adaptive SMC is illustrated by the simulation experiment in a numerical example, and its applicability is shown in the construction of an active suspension system for one-wheel car models.