Volume 26, 2020
|Number of page(s)||33|
|Published online||10 December 2020|
Singular extremals in L1-optimal control problems: sufficient optimality conditions*
Université de Toulon, Aix Marseille Univ, CNRS, LIS,
2 DiMaI, Università di Firenze, 50139 Firenze, Italy.
** Corresponding author: firstname.lastname@example.org
Accepted: 23 April 2020
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.
Mathematics Subject Classification: 49J15 / 49J30 / 49K30
Key words: Sufficient optimality conditions / control-affine systems / singular control / L1 minimisation / minimum fuel problem
© The authors. Published by EDP Sciences, SMAI 2020
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