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Multiobjective Stochastic Control in Fluid Dynamics via Game Theory Approach: Application to the Periodic Burgers Equation

Author

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  • A. M. Croicu

    (Kennesaw State University)

  • M. Y. Hussaini

    (Florida State University)

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.

Suggested Citation

  • A. M. Croicu & M. Y. Hussaini, 2008. "Multiobjective Stochastic Control in Fluid Dynamics via Game Theory Approach: Application to the Periodic Burgers Equation," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 501-514, December.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:3:d:10.1007_s10957-008-9416-0
    DOI: 10.1007/s10957-008-9416-0
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    References listed on IDEAS

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    1. C. González-Alcón & J. Sicilia & J. A. Álvarez, 1999. "Nash Equilibria in a Differential Game of Economic Growth," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 337-357, November.
    2. K. Kunisch & S. Volkwein, 1999. "Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 345-371, August.
    3. A.R. Kian & J.B. Cruz & M. A. Simaan, 2002. "Stochastic Discrete-Time Nash Games with Constrained State Estimators," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 171-188, July.
    4. A.M. Ramos & R. Glowinski & J. Periaux, 2002. "Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach," Journal of Optimization Theory and Applications, Springer, vol. 112(3), pages 499-516, March.
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    Cited by:

    1. Jimenez Edwin & Lay Nathan & Hussaini M. Yousuff, 2010. "A systematic study of efficient sampling methods to quantify uncertainty in crack propagation and the Burgers equation," Monte Carlo Methods and Applications, De Gruyter, vol. 16(1), pages 69-93, January.

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