Gain adaptation for continuous sliding mode control

In this paper a novel adaptive sliding mode controller design is presented for robust control of nonlinear uncertain systems. A continuous control law to compensate for the uncertainties is first developed that is completely free from chattering. Focusing on the relation between the tried gain value and the resultant sliding variable, a new method for estimating the uncertainty bounds is then derived, leading to an adaptive law for gain-tuning by which the error eventually lies within a user-specified region in a finite time. Unlike other existing approaches, the new adaptive rule only requires the magnitude of the control input in the previous time step, which greatly eases the application of the proposed algorithm to real-world systems. An inverted pendulum system is simulated to demonstrate the accuracy and effectiveness of the proposed control strategy.