Adaptive Second-order Sliding Mode Control: A Lyapunov Approach

This note proposes an adaptive second-order sliding mode (ASOSM) controller design by means of the Lyapunov method. The notable feature of the proposed algorithm is that it only needs boundedness of the uncertainties, while boundedness of the derivatives of uncertainties is not demanded. Under the proposed ASOSM control scheme, the gain can be dynamically tuned, which avoids gain overestimation. The finite-time stability of the closed-loop ASOSM dynamics is proved via the Lyapunov theory. Finally, the simulation results are shown to validate the theoretical analysis.