Optimal control of a semilinear parabolic equation with singular arcs

Joseph Frederic Bonnans 1, 2
1 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 develops a theory of singular arc, and the corresponding second order necessary and sufficient conditions, for the optimal control of a semilinear parabolic equation with scalar control applied on the r.h.s. We obtain in particular an extension of Kelley's condition, and the characterization of a quadratic growth property for a weak norm.
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Joseph Frederic Bonnans. Optimal control of a semilinear parabolic equation with singular arcs. Optimization Methods and Software, Taylor & Francis, 2014, 29 (2), pp.964-978. ⟨10.1080/10556788.2013.830220⟩. ⟨hal-00740698v2⟩

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