Regularity along optimal trajectories of the value function of a Mayer problem

Carlo Sinestrari

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 10, Issue: 4, page 666-676
  • ISSN: 1292-8119

Abstract

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We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.

How to cite

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Sinestrari, Carlo. "Regularity along optimal trajectories of the value function of a Mayer problem." ESAIM: Control, Optimisation and Calculus of Variations 10.4 (2010): 666-676. <http://eudml.org/doc/90750>.

@article{Sinestrari2010,
abstract = { We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system. },
author = {Sinestrari, Carlo},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; value function; semiconcavity.; optimal control; semiconcavity},
language = {eng},
month = {3},
number = {4},
pages = {666-676},
publisher = {EDP Sciences},
title = {Regularity along optimal trajectories of the value function of a Mayer problem},
url = {http://eudml.org/doc/90750},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Sinestrari, Carlo
TI - Regularity along optimal trajectories of the value function of a Mayer problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 4
SP - 666
EP - 676
AB - We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.
LA - eng
KW - Optimal control; value function; semiconcavity.; optimal control; semiconcavity
UR - http://eudml.org/doc/90750
ER -

References

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