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Singular extremals in L^1 optimal control problems: sufficient optimality conditions

Abstract : In this paper we are concerned with generalised L 1-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 proven by means of Hamiltonian methods. As a byproduct of the result, we provide an explicit invariant formula for the second variation along the singular arc.
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https://hal.archives-ouvertes.fr/hal-02283396
Contributor : Francesca Carlotta Chittaro <>
Submitted on : Tuesday, September 10, 2019 - 5:38:21 PM
Last modification on : Friday, December 11, 2020 - 3:12:59 AM

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  • HAL Id : hal-02283396, version 1

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Francesca Chittaro, Laura Poggiolini. Singular extremals in L^1 optimal control problems: sufficient optimality conditions. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2020, 26. ⟨hal-02283396⟩

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