Second-order sufficient conditions for strong solutions to optimal control problems

J. Frédéric Bonnans; Xavier Dupuis; Laurent Pfeiffer

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 3, page 704-724
  • ISSN: 1292-8119

Abstract

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In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure a fortiori that the reference trajectory is a bounded strong solution. Our proof relies on a decomposition principle, which is a particular second-order expansion of the Lagrangian of the problem.

How to cite

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Frédéric Bonnans, J., Dupuis, Xavier, and Pfeiffer, Laurent. "Second-order sufficient conditions for strong solutions to optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 20.3 (2014): 704-724. <http://eudml.org/doc/272895>.

@article{FrédéricBonnans2014,
abstract = {In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure a fortiori that the reference trajectory is a bounded strong solution. Our proof relies on a decomposition principle, which is a particular second-order expansion of the Lagrangian of the problem.},
author = {Frédéric Bonnans, J., Dupuis, Xavier, Pfeiffer, Laurent},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal control; second-order sufficient conditions; quadratic growth; bounded strong solutions; Pontryagin multipliers; pure state and mixed control-state constraints; decomposition principle; second-order sufficient optimalty conditions},
language = {eng},
number = {3},
pages = {704-724},
publisher = {EDP-Sciences},
title = {Second-order sufficient conditions for strong solutions to optimal control problems},
url = {http://eudml.org/doc/272895},
volume = {20},
year = {2014},
}

TY - JOUR
AU - Frédéric Bonnans, J.
AU - Dupuis, Xavier
AU - Pfeiffer, Laurent
TI - Second-order sufficient conditions for strong solutions to optimal control problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2014
PB - EDP-Sciences
VL - 20
IS - 3
SP - 704
EP - 724
AB - In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure a fortiori that the reference trajectory is a bounded strong solution. Our proof relies on a decomposition principle, which is a particular second-order expansion of the Lagrangian of the problem.
LA - eng
KW - optimal control; second-order sufficient conditions; quadratic growth; bounded strong solutions; Pontryagin multipliers; pure state and mixed control-state constraints; decomposition principle; second-order sufficient optimalty conditions
UR - http://eudml.org/doc/272895
ER -

References

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