Skip to Main content Skip to Navigation
Book sections

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

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.
Document type :
Book sections
Complete list of metadata

Cited literature [17 references]  Display  Hide  Download

https://hal.inria.fr/hal-01088904
Contributor : Helene Frankowska <>
Submitted on : Saturday, November 29, 2014 - 2:40:33 AM
Last modification on : Tuesday, December 8, 2020 - 3:36:19 AM
Long-term archiving on: : Friday, April 14, 2017 - 11:20:15 PM

File

1HFNO-10-11-14Version courte.p...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01088904, version 1

Citation

Hélène Frankowska, Nikolai 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⟩

Share

Metrics

Record views

396

Files downloads

995