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

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 secondorder sufficient conditio...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 20; no. 1; pp. 104 - 129
Main Author: Hermant, Audrey
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Subjects:
Boundary value problems
Contact
Mathematics
Multipliers
Norms
Optimal control
Optimization
Optimization and Control
Ordinary differential equations
Perturbation methods
Regularity
Stability
Studies
alternative formulation
uniform quadratic growth
Optimal control
stability analysis
second-order state constraint
strong regularity
sufficient second-order optimality condition
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary: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 secondorder 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^sup 2^ norm, and Holder continuous in the L∞ norm. We use a generalized implicit function theorem in metric spaces by Dontchev and Hager [SIAM J. Control Optim., 36 (1998), pp. 698-718]. 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. [PUBLICATION ABSTRACT]
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ISSN:1052-6234
1095-7189
DOI:10.1137/070707993