# Stability Analysis of Optimal Control Problems with a Second-order State Constraint

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 gives stability results for nonlinear optimal control problems subject to a regular state constraint of second-order. The strengthened Legendre-Clebsch condition is assumed to hold, and no assumption on the structure of the contact set is made. Under a weak second-order sufficient condition (taking into account the active constraints), we show that the solutions are Lipschitz continuous w.r.t. the perturbation parameter in the $L^2$ norm, and Hölder continuous in the $L^\infty$ norm. We use a generalized implicit function theorem in metric spaces by Dontchev and Hager [SIAM J. Control Optim., 1998]. The difficulty is that multipliers associated with second-order state constraints have a low regularity (they are only bounded measures). We obtain Lipschitz stability of a primitive'' of the state constraint multiplier.
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Journal articles

Cited literature [27 references]

https://hal.inria.fr/inria-00186968
Contributor : Audrey Hermant <>
Submitted on : Wednesday, November 14, 2007 - 11:12:49 AM
Last modification on : Monday, September 30, 2019 - 10:46:02 AM
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### Citation

Audrey Hermant. Stability Analysis of Optimal Control Problems with a Second-order State Constraint. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2009, 20 (1), pp.104-129. ⟨10.1137/070707993⟩. ⟨inria-00186968v2⟩

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