Development of an adaptive radial basis function neural network estimator-based continuous sliding mode control for uncertain nonlinear systems.

In this paper an adaptive neural network (NN)-based nonlinear controller is proposed for trajectory tracking of uncertain nonlinear systems. The adopted control algorithm combines a continuous second-order sliding mode control (CSOSMC), the radial basis function neural network (RBFNN) and the adaptive control methodology. First, a second-order sliding mode control scheme (SOSMC), which is published recently in literature for linear uncertain systems, is extended for nonlinear uncertain systems. Second, an adaptive radial basis function neural network estimator-based continuous second order sliding mode control algorithm (CSOSMC-ANNE) is adopted. In CSOSMC-ANNE control methodology, a radial basis function neural network with adaptive parameters is exploited to approximate the unknown system parameters and improve performance against perturbations. Also, the discontinuous switching control of SOSMC is supplanted with a smooth continuous control action to completely eliminate the chattering phenomenon. The convergence and global stability of the closed-loop system are proved using Lyapunov stability method. Numerical computer simulations, with dynamical model of the nonlinear inverted pendulum system, are presented to demonstrate the effectiveness and advantages of the presented control scheme.