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 proved 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.
SINGULAR EXTREMALS IN L¹-OPTIMAL CONTROL PROBLEMS: SUFFICIENT OPTIMALITY CONDITIONS / Francesca Carlotta Chittaro; Laura Poggiolini. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 26:(2020), pp. 1-33. [10.1051/cocv/2020023]
SINGULAR EXTREMALS IN L¹-OPTIMAL CONTROL PROBLEMS: SUFFICIENT OPTIMALITY CONDITIONS
Laura Poggiolini
2020
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 proved 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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