Stability Analysis of Optimal Control Problems with a Second-order State Constraint - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles SIAM Journal on Optimization Year : 2009

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

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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Dates and versions

inria-00186968 , version 1 (13-11-2007)
inria-00186968 , version 2 (14-11-2007)

Identifiers

Cite

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