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Journal of Optimization Theory and Applications

, Volume 180, Issue 1, pp 207–234 | Cite as

Strong Local Optimality for Generalized L1 Optimal Control Problems

  • Francesca C. Chittaro
  • Laura PoggioliniEmail author
Article

Abstract

In this paper, we analyze control-affine optimal control problems with a cost functional involving the absolute value of the control. The Pontryagin extremals associated with such systems are given by (possible) concatenations of bang arcs with singular arcs and with zero control arcs, that is, arcs where the control is identically zero. Here, we consider Pontryagin extremals given by a bang-zero control-bang concatenation. We establish sufficient optimality conditions for such extremals, in terms of some regularity conditions and of the coerciveness of a suitable finite-dimensional second variation.

Keywords

Optimal control Sufficient conditions Hamiltonian methods Sparse control 

Mathematics Subject Classification

49K15 49K30 

Notes

Acknowledgements

This work was supported by the projects “Dinamiche non autonome, sistemi Hamil- toniani e teoria del controllo” (GNAMPA 2015), “Dinamica topologica, sistemi Hamiltoniani e teoria del controllo” (GNAMPA 2016), “Sistemi Dinamici, Teoria del Controllo e Applicazioni” (GNAMPA 2017) by Istituto Nazionale di Alta Matematica “Francesco Severi” and by UTLN–Appel à projet “Chercheurs invités”, Université de Toulon, years 2015, 2016 and 2017.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Aix Marseille Univ, Université de ToulonCNRS, LISMarseilleFrance
  2. 2.Dipartimento di Matematica e Informatica “Ulisse Dini”Università degli Studi di FirenzeFlorenceItaly

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