In this paper we give sufficient conditions for a Pontryagin extremal trajectory, consisting of two bang arcs followed by a partially or totally singular one, to be a strong local minimizer for a Mayer problem. The problem is defined on $mathbb{R}^n$ and the end-points constraints are of fixed-free type. We use a Hamiltonian approach and its connection with the second order conditions in the form of a linear quadratic accessory problem. An example is proposed. All the results are coordinate free so they also hold on a manifold.

Strong local optimality for a bang-bang-singular extremal: the fixed-free case / Laura Poggiolini; Gianna Stefani. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 1095-7138. - STAMPA. - 56(2018), pp. 2274-2294. [10.1137/17M1140248]

Strong local optimality for a bang-bang-singular extremal: the fixed-free case

Laura Poggiolini
;
Gianna Stefani
2018

Abstract

In this paper we give sufficient conditions for a Pontryagin extremal trajectory, consisting of two bang arcs followed by a partially or totally singular one, to be a strong local minimizer for a Mayer problem. The problem is defined on $mathbb{R}^n$ and the end-points constraints are of fixed-free type. We use a Hamiltonian approach and its connection with the second order conditions in the form of a linear quadratic accessory problem. An example is proposed. All the results are coordinate free so they also hold on a manifold.
56
2274
2294
Laura Poggiolini; Gianna Stefani
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1130218
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