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Dynamical systems‐based optimal control of incompressible fluids
Author(s) -
Hintermüller Michael,
Kunisch Karl,
Spasov Yulian,
Volkwein Stefan
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.725
Subject(s) - optimal control , dynamical systems theory , vortex , realization (probability) , compressibility , mathematics , regular polygon , function (biology) , tensor (intrinsic definition) , flow (mathematics) , computational fluid dynamics , mathematical optimization , numerical analysis , control theory (sociology) , computer science , control (management) , mathematical analysis , physics , mechanics , geometry , statistics , quantum mechanics , evolutionary biology , artificial intelligence , biology
For optimal control problems related to fluid flow the choice of an adequate cost functional for suppression of vortices is of significant importance. In this research we propose a cost functional based on a local dynamical systems characterization of vortices. The resulting functional is a non‐convex function of the velocity gradient tensor. The resulting optimality system describing first order necessary optimality conditions is derived, a possible strategy for numerical realization of the optimal control problem is provided and a numerical feasibility study is conducted. Copyright © 2004 John Wiley & Sons, Ltd.