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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Vydáno v:Mathematical programming Ročník 168; číslo 1-2; s. 717 - 757
Hlavní autoři: Aronna, M. Soledad, Bonnans, J. Frédéric, Kröner, Axel
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2018
Springer Nature B.V
Springer Verlag
Témata:
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
Wave equation
49K20
Partial differential equations
Heat equation
Optimal control
35L05
Second-order optimality conditions
35K05
Semigroup theory
90C48
Bilinear control systems
Goh transform
second-order optimality conditions
heat equation
bilinear control systems
wave equation
partial differential equations
semigroup theory
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-016-1093-4