Mean Field Type Control with Congestion

We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal con...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 73; no. 3; pp. 393 - 418
Main Authors Achdou, Yves, Laurière, Mathieu
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2016
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Congestion
Control
Control systems
Control theory
DUALITY
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
MATHEMATICAL SOLUTIONS
Mathematics
Mathematics and Statistics
MEAN-FIELD THEORY
Numerical and Computational Physics
OPTIMAL CONTROL
Optimization
PARTIAL DIFFERENTIAL EQUATIONS
Probability distribution
Simulation
Studies
Systems Theory
Theoretical
Uniqueness
35K40
Mean field type control
Weak solutions
49K20
49N70
Optimal control
35D30
35K55
35K65
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ISSN0095-4616
1432-0606
DOI10.1007/s00245-016-9342-8

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Summary:We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-016-9342-8