Multiobjective Stochastic Control in Fluid Dynamics via Game Theory Approach: Application to the Periodic Burgers Equation |
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Authors: | A M Croicu M Y Hussaini |
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Institution: | (1) Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, 30144-5591, USA;(2) School of Computational Science, Florida State University, Tallahassee, FL 32306-4120, USA |
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Abstract: | The purpose of the present work is to implement well-known statistical decision and game theory strategies into multiobjective
stochastic control problems of fluid dynamics. Such goal is first justified by the fact that deterministic (either singleobjective
or multiobjective) control problems that are obtained without taking into account the uncertainty of the model are usually
unreliable. Second, in most real-world problems, several goals must be satisfied simultaneously to obtain an optimal solution
and, as a consequence, a multiobjective control approach is more appropriate. Therefore, we develop a multiobjective stochastic
control algorithm for general fluid dynamics applications, based on the Bayes decision, adjoint formulation and the Nash equilibrium
strategies. The algorithm is exemplified by the multiobjective stochastic control of a periodic Burgers equation. |
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Keywords: | Stochastic Nash equilibrium Optimal control Expected value Adjoint system Burgers equation |
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