Second order analysis of state-constrained control-affine problems

Maria Soledad Aronna 1 J. Frederic Bonnans 2, 3 Bean San Goh 4
1 UCI - UMI CNRS-IMPA
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 Curtin University, Sarawak Malaysia
Abstract : In this article we establish new second order necessary and suffi-cient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.
Keywords : optimality conditions Optimal Control
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Journal articles
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Maria Soledad Aronna, J. Frederic Bonnans, Bean San Goh. Second order analysis of state-constrained control-affine problems. Mathematical Programming, Series A, Springer, 2016, 160 (1), pp.115-147. ⟨hal-01081111v2⟩

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