Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave EquationsReport as inadecuate




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1 FGV - Fundacao Getulio Vargas Rio de Janeiro 2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique 3 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, Univ. Paris-Saclay, ENSTA ParisTech - École Nationale Supérieure de Techniques Avancées, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7641

Abstract : In this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator, the control entering linearly in the cost function. We derive first and second order optimality conditions, taking advantage of the Goh transform. We then apply the results to the heat and wave equations.

Keywords : partial differential equations semigroup theory Optimal control bilinear control systems wave equation heat equation Goh transform second-order optimality conditions





Author: Maria Soledad Aronna - Joseph Fréderic Bonnans - Axel Kröner -

Source: https://hal.archives-ouvertes.fr/



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