New Class $\mathcal {K}_\infty$ Function-Based Adaptive Sliding Mode Control

Abstract

To reduce the chattering and overestimation phenomena existing in classical adaptive sliding mode control, this paper presents a new class <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {K}_\infty$</tex-math></inline-formula> function-based adaptive sliding mode control scheme. Two controllers are proposed in terms of concave and convex nonlinear functions to implement this kind of control structure. To avoid large initial control magnitudes, two modified control schemes are provided, which extend the proposed methodology to different scenarios. It is proven that the proposed controllers yield finite-time convergence to a real sliding mode. Finally, simulations and discussions are presented to show the advantages and effectiveness of the proposed control structure.