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Stability and Sensitivity Analysis for Optimal Control Problems with a First-order State Constraint having (nonessential) Touch Points

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. We show how to perform a sensitivity analysis that predicts which touch points will, under a small perturbation, become inactive, remain touch points or switch into boundary arcs. The main tools are the study of a quadratic tangent problem and the notion of strong regularity. The results can be interpreted as an extension of the shooting algorithm to the case when touch points occur for first-order state constraints. An illustrative example is given.
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https://hal.inria.fr/inria-00087573
Contributor : J. Frederic Bonnans Connect in order to contact the contributor
Submitted on : Wednesday, July 26, 2006 - 4:03:31 PM
Last modification on : Thursday, February 3, 2022 - 11:13:57 AM
Long-term archiving on: : Monday, September 20, 2010 - 4:37:05 PM

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  • HAL Id : inria-00087573, version 2

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J. Frederic Bonnans, Audrey Hermant. Stability and Sensitivity Analysis for Optimal Control Problems with a First-order State Constraint having (nonessential) Touch Points. [Research Report] 2006, pp.34. ⟨inria-00087573v2⟩

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