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

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.