Second-Order Necessary Optimality Conditions for the Mayer Problem Subject to a General Control Constraint - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Book Sections Year : 2015

Second-Order Necessary Optimality Conditions for the Mayer Problem Subject to a General Control Constraint

Hélène Frankowska
  • Function : Author
  • PersonId : 956269
Nikolai P. Osmolovskii
  • Function : Author
  • PersonId : 896684

Abstract

This paper is devoted to second-order necessary optimality conditions for the Mayer optimal control problem with an arbitrary closed control set U contained in a finite dimensional space. Admissible controls are supposed to be measurable and essentially bounded. Using second order tangents to U, we first show that if u(.) is an optimal control, then an associated quadratic functional should be nonnegative for all elements in the second order jets to U along u(.). Then we specify the obtained results in the case when U is given by a finite number of C^2-smooth inequalities with positively independent gradients of active constraints. The novelty of our approach is due, on one hand, to the arbitrariness of U. On the other hand, the proofs we propose are quite straightforward and do not use embedding of the problem into a class of infinite dimensional mathematical programming type problems. As an application we derive new second-order necessary conditionsfor a free end-time optimal control problem in the case when anoptimal control is piecewise Lipschitz.
Fichier principal
Vignette du fichier
1HFNO-10-11-14Version courte.pdf (354.79 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01088904 , version 1 (29-11-2014)

Identifiers

  • HAL Id : hal-01088904 , version 1

Cite

Hélène Frankowska, Nikolai P. Osmolovskii. Second-Order Necessary Optimality Conditions for the Mayer Problem Subject to a General Control Constraint. Bettiol, P., Cannarsa, P., Colombo, G., Motta, M., Rampazzo, F. (Eds.). Analysis and Geometry in Control Theory and its Applications, 12, Springer Verlag, 2015, Springer INDAM series, 978-3-319-06916-6. ⟨hal-01088904⟩
199 View
304 Download

Share

Gmail Facebook X LinkedIn More