An Optimization Perspective on Discrete-Time Sliding Modes: When Proximal-Point Algorithms Meet Set-Valued Systems
Year: 2025
Type: article
Abstract: This article investigates how classical discontinuous sliding-mode signals can be more effectively understood and implemented using principles from optimization and convex analysis. For continuous-time systems, the study identifies energy dissipation as a fundamental aspect of the method. In discrete-time implementations, the research shows that employing the well-established backward-Euler discretization allows us to preserve robustness against matched disturbances as well as finite-time convergence whilst drastically reducing high-frequency oscillations (known as the chattering phenomenon). A significant contribution of this work is establishing a clear connection between control methodologies and optimization algorithms, using Proximal-Point Algorithms (PPA) and proximal operators. By creating this link, powerful optimization techniques can be utilized to simplify analysis and enhance the design of control systems.
Source: IEEE Control Systems
Institutions: University of Cambridge, Instituto Politécnico Nacional, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Institut polytechnique de Grenoble, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Laboratoire Jean Kuntzmann, Université Grenoble Alpes
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414499422