Adaptive Integral Sliding Mode Control in the Presence of State-Dependent Uncertainty
Peng Li, Di Liu, Simone Baldi
Abstract
Adaptive integral sliding mode control (AISMC) is an extension of adaptive sliding mode control which is a way to ensure sliding motion while handling system uncertainties. However, conventional AISMC formulations require to different extent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of the system uncertainty: either the upper bound of the uncertainty or of its time derivative are assumed to be bounded <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> , or the uncertainty is assumed to be parametrized by some structure-dependent factorization. This work proposes a variant of AISMC with reduced <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of the system uncertainty: it is shown that Euler–Lagrange dynamics typical of sliding mode literature admit a structure-independent parametrization of the system uncertainty. This parametrization is not the result of structural knowledge, but it comes from basic properties of Euler–Lagrange dynamics, valid independently on the structure of the system. The AISMC control method arising from this parametrization is analyzed in the Lyapunov stability framework, and validated in systems with different structures: a surface vessel and an aerial vehicle.