Second-order necessary conditions in Pontryagin form for optimal control problems

J. Frederic Bonnans 1, 2 Xavier Dupuis 1, 2 Laurent Pfeiffer 1, 2
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
Abstract : In this report, we state and prove first- and second-order necessary conditions in Pontryagin form for optimal control problems with pure state and mixed control-state constraints. We say that a Lagrange multiplier of an optimal control problem is a Pontryagin multiplier if it is such that Pontryagin's minimum principle holds, and we call optimality conditions in Pontryagin form those which only involve Pontryagin multipliers. Our conditions rely on a technique of partial relaxation, and apply to Pontryagin local minima.
Document type :
Journal articles
Complete list of metadatas

https://hal.inria.fr/hal-00825273
Contributor : Xavier Dupuis <>
Submitted on : Thursday, May 23, 2013 - 12:36:58 PM
Last modification on : Monday, September 30, 2019 - 10:46:02 AM
Long-term archiving on : Saturday, August 24, 2013 - 5:20:30 AM

File

RR-8306.pdf
Files produced by the author(s)

Identifiers

Citation

J. Frederic Bonnans, Xavier Dupuis, Laurent Pfeiffer. Second-order necessary conditions in Pontryagin form for optimal control problems. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (6), pp.3887-3916. ⟨10.1137/130923452⟩. ⟨hal-00825273⟩

Share

Metrics

Record views

881

Files downloads

626