Simple Adaptive Methodology for Chattering-free Sliding Mode Control

This paper presents a new adaptive methodology for sliding mode control of a nonlinear dynamical system in the presence of unknown, but bounded uncertainties. A continuous control law is first developed to compensate for the uncertainties and this Lyapunov-based approach eliminates chattering by replacing a discontinuous signum function with a continuous function. By investigating the relation between the estimated gain with respect to the real unknown uncertainties and the resultant sliding variable, a new adaptive tuning law is obtained to ensure that the gain update is performed in real time and the resulting error is bounded within a user-specified value. The proposed adaptive algorithm is simple and easy to implement, and an inverted pendulum problem serves to demonstrate the accuracy and effectiveness of the control methodology proposed herein.