Work

Sparsity and L 1 -optimal control for linear control systems

Year: 2025

Type: article

Abstract: For linear time-invariant systems, we take an interest in sparse controls, i.e., those whose support (or L 0 -norm) is of minimal Lebesgue measure. We propose to extend this research to Radon measures and, in particular, to controls presenting Dirac impulses. Then, we can find a minimizer which is purely impulsive (and so with a null support) and prove that there is no gap when we extend the problem from L 1 -controls to Radon measures. To refine our research, this reasoning leads us to study the minimization problems for L 1 and measure norms. We prove that impulsive controls are still pertinent for these problems: once again, we can find a minimizer and prove that there is no gap. In addition to the existence of a solution, we show that, by extending the research to Radon measures, we can find a solution of L 0 and L 1 -minimization problems in the form of a finite linear combination of Dirac impulses, and we give an expression of the maximal number of these impulses. We also propose an algorithm in order to compute an impulsive solution of the measure norm minimization problem.

Source: Automatica

DOI: 10.1016/j.automatica.2025.112672

Authors: Pierre Cavaré, Marc Jungers, Jérôme Lohéac

Institutions: Centre National de la Recherche Scientifique, CRAN, Université de Lorraine

Language: English

Topic: Advanced Control Systems Optimization

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,760

Funders: Université de Lorraine, Agence Nationale de la Recherche