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Preprints, Working Papers, ... Year : 2023

When proximal-point algorithms meet set-valued systems. An Optimization point of view of discrete-time sliding modes

Abstract

This article is largely concerned with the relationships between the implicit (backward) discretization of set-valued sliding-mode systems (for control, state observation, or differentiation), and proximal-point algorithms of optimization. It is shown that using well-known notions like maximal monotonicity, proximal and resolvent operators, and Yosida approximations, it is possible to embed implicit time-discretization methods into the unified framework of proximal-point algorithms. This is illustrated with first-order and higher-order sliding-mode systems. Passivity is shown to play an important role. Robust, time-varying, Hamiltonian and high-order extensions of the classical proximal-point algorithm are introduced. Particular attention is given to the use of splitting methods to resolve computational issues related to implementation.
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hal-04362282 , version 1 (22-12-2023)

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  • HAL Id : hal-04362282 , version 1

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Félix Miranda-Villatoro, Fernando Castaños, Bernard Brogliato. When proximal-point algorithms meet set-valued systems. An Optimization point of view of discrete-time sliding modes. 2023. ⟨hal-04362282⟩
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