A novel adaptive-gain higher-order sliding mode controller and its parameters tuning

This paper proposes an adaptive higher-order sliding mode control for nonlinear uncertain systems. First, a continuous higher-order sliding mode surface is constructed by means of the homogeneity theory. Based on a concept of stability factor, the quantitative relation between domain of attraction and coefficients of the sliding surface is established, and then a novel parameter tuning principle of the designed sliding surface is formulated to achieve the globally finite-time stability of sliding system, which enjoys the advantages of simplicity and effectiveness for stabilizing intrinsically nonlinear manifolds compared with Hurwitz criterion. Moreover, by using a multiplicative iteration method, an adaptation algorithm is developed to search the minimal admissible solution of switching gain on the premise of preserving the sliding mode, and the adaptive gain can realize its self-tuning regulation for adapting to the variation of disturbances so as to significantly attenuate chattering. Finally, simulation results on a magnetic suspension system and a high-order integrator are presented to validate the effectiveness of the proposed control scheme.