Optimal control of infinite dimensional bilinear systems: application to the heat and wave equations

Optimal control of infinite dimensional bilinear systems: application to the heat and wave equations

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....

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Veröffentlicht in:Mathematical programming 2018-03, Vol.168 (1-2), p.717-757
Hauptverfasser: Aronna, M. Soledad, Bonnans, J. Frédéric, Kröner, Axel
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Full Length Paper
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Nonlinear programming
Numerical Analysis
Operators (mathematics)
Optimal control
Optimization
Optimization and Control
Theoretical
Wave equations
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Beschreibung
Zusammenfassung: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.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-1093-4