Adaptive Discrete Sliding Mode Control for Mechanical Systems with Mismatched Uncertainties

This paper is concerned with an adaptive discrete sliding mode control (SMC) for mechanical systems with mismatched uncertainties. It is assumed that the mechanical systems to be considered here are described by a discrete-time state equation with uncertainties found in unmodeled dynamics and external disturbances, and the states are measured in the contamination with independent random noises. The uncertainties are expressed in a parameterized form, and the estimates for the states and the uncertainties are taken by using the proposed weighted least squares estimator (WLSE). The proposed adaptive discrete SMC is constructed on the basis of the estimates obtained by the proposed WLSE. It is verified by using the Lyapunov method that the estimation error equation is asymptotically stable, and the mechanical systems are ultimately bounded under the action of the proposed adaptive discrete SMC. The effectiveness of the proposed method is indicated by the simulation experiment in the application to the design of an active suspension system for one-wheel car models.