Singular extremals in L^1 optimal control problems: sufficient optimality conditions
| Autor: | Laura Poggiolini, Francesca Chittaro |
|---|---|
| Přispěvatelé: | Contrôle et Diagnostic pour l’Environnement (CDE), Laboratoire d'Informatique et Systèmes (LIS), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Université de Toulon (UTLN), Dipartimento di Matematica Applicata [Firenze] (DMA), Università degli Studi di Firenze = University of Florence [Firenze] (UNIFI), Università degli Studi di Firenze = University of Florence [Firenze], Università degli Studi di Firenze = University of Florence (UniFI) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Control and Optimization 0211 other engineering and technologies 02 engineering and technology control-affine systems L 1 minimisation 020901 industrial engineering & automation L1 minimisation FOS: Mathematics Sufficient optimality conditions Applied mathematics [MATH]Mathematics [math] minimum fuel problem Mathematics - Optimization and Control 1991 Mathematics Subject Classification. 49J15 Mathematics 021103 operations research Computer Science::Information Retrieval singular control Optimal control Singular control Computational Mathematics Optimization and Control (math.OC) Control and Systems Engineering [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 49J30 Hamiltonian (control theory) 49K30 sufficient optimality conditions |
| Zdroj: | ESAIM: Control, Optimisation and Calculus of Variations ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2020, 26, pp.99. ⟨10.1051/cocv/2020023⟩ ESAIM: Control, Optimisation and Calculus of Variations, 2020, 26, pp.99. ⟨10.1051/cocv/2020023⟩ |
| ISSN: | 1292-8119 1262-3377 |
| DOI: | 10.1051/cocv/2020023⟩ |
| Popis: | In this paper we are concerned with generalisedL1-minimisation problems,i.e.Bolza problems involving the absolute value of the control with a control-affine dynamics. We establish sufficient conditions for the strong local optimality of extremals given by the concatenation of bang, singular and inactive (zero) arcs. The sufficiency of such conditions is proved by means of Hamiltonian methods. As a by-product of the result, we provide an explicit invariant formula for the second variation along the singular arc. |
| Databáze: | OpenAIRE |
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