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Reports (Research Report) Year : 2006

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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Dates and versions

inria-00087573 , version 1 (25-07-2006)
inria-00087573 , version 2 (26-07-2006)

Identifiers

  • HAL Id : inria-00087573 , version 2

Cite

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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