Differential continuation for regular optimal control problems

Regular control problems in the sense of the Legendre condition are defined, and second-order necessary and sufficient optimality conditions in this class are reviewed. Adding a scalar homotopy parameter, differential pathfollowing is introduced. The previous sufficient conditions ensure the definit...

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Bibliographic Details
Published in:Optimization methods & software 2012-04, Vol.27 (2), p.177-196
Main Authors: Caillau, J.-B., Cots, O., Gergaud, J.
Format: Article
Language:English
Subjects:
49-04
automatic differentiation
conjugate points
differential homotopy
Mathematics
Operations research
optimal control
Optimization
Optimization and Control
second-order conditions
Studies
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Summary:Regular control problems in the sense of the Legendre condition are defined, and second-order necessary and sufficient optimality conditions in this class are reviewed. Adding a scalar homotopy parameter, differential pathfollowing is introduced. The previous sufficient conditions ensure the definiteness and regularity of the path. The role of AD for the implementation of this approach is discussed, and two examples excerpted from quantum and space mechanics are detailed.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2011.593625