Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods

Joseph Frédéric Bonnans; Audrey Hermant

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 4, page 825-863
  • ISSN: 1292-8119

Abstract

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The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of (nonessential) touch points, the arc structure of the trajectory is not stable. Under some reasonable assumptions, we show that boundary arcs are structurally stable, and that touch point can either remain so, vanish or be transformed into a single boundary arc. Assuming a weak second-order optimality condition (equivalent to uniform quadratic growth), stability and sensitivity results are given. The main tools are the study of a quadratic tangent problem and the notion of strong regularity. Those results enable us to design a new continuation algorithm, presented at the end of the paper, that handles automatically changes in the structure of the trajectory.

How to cite

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Bonnans, Joseph Frédéric, and Hermant, Audrey. "Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 825-863. <http://eudml.org/doc/250376>.

@article{Bonnans2008,
abstract = { The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of (nonessential) touch points, the arc structure of the trajectory is not stable. Under some reasonable assumptions, we show that boundary arcs are structurally stable, and that touch point can either remain so, vanish or be transformed into a single boundary arc. Assuming a weak second-order optimality condition (equivalent to uniform quadratic growth), stability and sensitivity results are given. The main tools are the study of a quadratic tangent problem and the notion of strong regularity. Those results enable us to design a new continuation algorithm, presented at the end of the paper, that handles automatically changes in the structure of the trajectory. },
author = {Bonnans, Joseph Frédéric, Hermant, Audrey},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; first-order state constraint; strong regularity; sensitivity analysis; touch point; homotopy method; optimal control; touch point},
language = {eng},
month = {2},
number = {4},
pages = {825-863},
publisher = {EDP Sciences},
title = {Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods},
url = {http://eudml.org/doc/250376},
volume = {14},
year = {2008},
}

TY - JOUR
AU - Bonnans, Joseph Frédéric
AU - Hermant, Audrey
TI - Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2008/2//
PB - EDP Sciences
VL - 14
IS - 4
SP - 825
EP - 863
AB - The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of (nonessential) touch points, the arc structure of the trajectory is not stable. Under some reasonable assumptions, we show that boundary arcs are structurally stable, and that touch point can either remain so, vanish or be transformed into a single boundary arc. Assuming a weak second-order optimality condition (equivalent to uniform quadratic growth), stability and sensitivity results are given. The main tools are the study of a quadratic tangent problem and the notion of strong regularity. Those results enable us to design a new continuation algorithm, presented at the end of the paper, that handles automatically changes in the structure of the trajectory.
LA - eng
KW - Optimal control; first-order state constraint; strong regularity; sensitivity analysis; touch point; homotopy method; optimal control; touch point
UR - http://eudml.org/doc/250376
ER -

References

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