# Well-Posedness of the Shooting Algorithm for State Constrained Optimal Control Problems with a Single Constraint and Control

Abstract : This paper deals with the shooting algorithm for optimal control problems with a scalar control and a regular scalar state constraint. Additional conditions are displayed, under which the so-called alternative formulation is equivalent to Pontryagin's minimum principle. The shooting algorithm appears to be well-posed (invertible Jacobian), if and only if (i) the no-gap second order sufficient optimality condition holds, and (ii) when the constraint is of order $q \geq3$, there is no boundary arc. Stability and sensitivity results without strict complementarity at touch points are derived using Robinson's strong regularity theory, under a minimal second-order sufficient condition. The directional derivatives of the control and state are obtained as solutions of a linear quadratic problem.
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https://hal.inria.fr/inria-00071379
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 5:01:26 PM
Last modification on : Friday, May 25, 2018 - 12:02:04 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:08:22 PM

### Identifiers

• HAL Id : inria-00071379, version 1

### Citation

J. Frederic Bonnans, Audrey Hermant. Well-Posedness of the Shooting Algorithm for State Constrained Optimal Control Problems with a Single Constraint and Control. [Research Report] RR-5889, INRIA. 2006. ⟨inria-00071379⟩

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