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Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave Equations

Maria Soledad Aronna 1 Joseph Fréderic Bonnans 2, 3 Axel Kröner 2, 3 
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
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 : Goh transform heat equation wave equation partial differential equations semigroup theory Optimal control bilinear control systems second-order optimality conditions
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Submitted on : Monday, September 5, 2016 - 3:07:48 PM
Last modification on : Thursday, January 20, 2022 - 5:31:30 PM
Long-term archiving on: : Tuesday, December 6, 2016 - 1:43:28 PM

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Maria Soledad Aronna, Joseph Fréderic Bonnans, Axel Kröner. Optimal Control of Infinite Dimensional Bilinear Systems: Application to the Heat and Wave Equations. Mathematical Programming, Springer Verlag, 2018, 168 (1-2), pp.717-757. ⟨hal-01273496v2⟩

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