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Optimal control of electrorheological fluids through the action of electric fields

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  • Juan De Los Reyes
  • Irwin Yousept

Abstract

This paper is concerned with an optimal control problem of steady-state electrorheological fluids based on an extended Bingham model. Our control parameters are given by finite real numbers representing applied direct voltages, which enter in the viscosity of the electrorheological fluid via an electrostatic potential. The corresponding optimization problem belongs to a class of nonlinear optimal control problems of variational inequalities with control in the coefficients. We analyze the associated variational inequality model and the optimal control problem. Thereafter, we introduce a family of Huber-regularized optimal control problems for the approximation of the original one and verify the convergence of the regularized solutions. Differentiability of the solution operator is proved and an optimality system for each regularized problem is established. In the last part of the paper, an algorithm for the numerical solution of the regularized problem is constructed and numerical experiments are carried out. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Juan De Los Reyes & Irwin Yousept, 2015. "Optimal control of electrorheological fluids through the action of electric fields," Computational Optimization and Applications, Springer, vol. 62(1), pages 241-270, September.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:1:p:241-270
    DOI: 10.1007/s10589-014-9705-5
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    References listed on IDEAS

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    1. Irwin Yousept, 2012. "Optimal control of Maxwell’s equations with regularized state constraints," Computational Optimization and Applications, Springer, vol. 52(2), pages 559-581, June.
    2. Juan Reyes, 2012. "Optimization of mixed variational inequalities arising in flow of viscoplastic materials," Computational Optimization and Applications, Springer, vol. 52(3), pages 757-784, July.
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