Well-Posedness of the Shooting Algorithm for State Constrained Optimal Control Problems with a Single Constraint and Control - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2006

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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Dates and versions

inria-00071379 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00071379 , version 1

Cite

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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