Adaptive backstepping sliding mode control with Gaussian networks for a class of nonlinear systems with mismatched uncertainties

This paper is concerned with the adaptive sliding-mode control of a class of nonlinear systems in nonlinear parametric-pure-feedback form with mismatched uncertainties. Backstepping design procedure is applied, which leads to a new adaptive sliding-mode control. Gaussian radial-basis-function networks are used to approximate the unknown system dynamics. A new growing scheme of the Gaussian networks is proposed. The networks start with a loose structure in order to reduce the computational effort. More nodes are added to the networks progressively in order to improve the transient behaviour. With ideal sliding mode, asymptotic stability is reached. The performance of the control scheme is illustrated by simulation studies.