Adaptive sliding mode and second order sliding mode control with applications: a survey

Control under uncertainty is one of the main topics of the modern control theory. The idea of sliding mode and second order sliding mode control (SMC/2-SMC) is to drive the system trajectory to properly chosen constraints (sliding manifold) in finite time and keeping it there for all subsequent time by means of high-frequency switching control. Adaptive SMC/2-SMC has been of great interest in the sliding mode control community during the last 15 years due to its ability to handle perturbations with unknown bounds while mitigating chattering, if the adaptive control gains are not overestimated. This paper presents an overview of the adaptive SMC/2-SMC algorithms. A number of applications are also discussed. The literature in the area is presented in the context of continuing developments in the theory and application of adaptive SMC/2-SMC. Copyright (c) 2023 The Authors.