Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint

Audrey Hermant 1, 2, *
* Corresponding author
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : This paper deals with optimal control problems with a regular second-order state constraint and a scalar control, satisfying the strengthened Legendre-Clebsch condition. We study the stability of structure of stationary points. It is shown that under a uniform strict complementarity assumption, boundary arcs are stable under sufficiently smooth perturbations of the data. On the contrary, nonreducible touch points are not stable under perturbations. We show that under some reasonable conditions, either a boundary arc or a second touch point may appear. Those results allow us to design an homotopy algorithm which automatically detects the structure of the trajectory and initializes the shooting parameters associated with boundary arcs and touch points.
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Submitted on : Wednesday, September 3, 2008 - 9:36:02 AM
Last modification on : Friday, April 19, 2019 - 3:24:49 PM
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Audrey Hermant. Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint. Applied Mathematics and Optimization, Springer Verlag (Germany), 2010, 61 (1), pp.85-127. ⟨10.1007/s00245-009-9076-y⟩. ⟨inria-00316281⟩

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