Singular extremals in L 1 -optimal control problems: sufficient optimality conditions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 99.

In this paper we are concerned with generalised L1-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.

DOI : 10.1051/cocv/2020023
Classification : 49J15, 49J30, 49K30
Mots-clés : Sufficient optimality conditions, control-affine systems, singular control, $L^1$ minimisation, minimum fuel problem 
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     author = {Chittaro, Francesca C. and Poggiolini, Laura},
     title = {Singular extremals in $L^1$-optimal control problems: sufficient optimality conditions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
     doi = {10.1051/cocv/2020023},
     mrnumber = {4185063},
     zbl = {1471.49004},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2020023/}
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Chittaro, Francesca C.; Poggiolini, Laura. Singular extremals in $L^1$-optimal control problems: sufficient optimality conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 99. doi : 10.1051/cocv/2020023. http://www.numdam.org/articles/10.1051/cocv/2020023/

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This work has been supported by “National Group for Mathematical Analysis, Probability and their Applications” (GNAMPA-INdAM), by UTLN−Appel à projet “Chercheurs invités”, Université de Toulon, by Progetto Internazionalizzazione, Università degli Studi di Firenze and by CARTT - IUT de Toulon.