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Optimal distributed control of nonlinear Cahn–Hilliard systems with computational realization

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Abstract

The goal of this work is to present some optimal control aspects of distributed systems described by nonlinear Cahn–Hilliard equations (CH). Theoretical conclusions on distributed control of CH system associated with quadratic criteria are obtained by the variational theory (see [17]). A computational result is stated by a new semi-discrete algorithm, constructed on the basis of the finite-element method with the updated (nonlinear) conjugate gradient method for minimizing the performance index efficiently. Finally, the implementation of a laboratory demonstration is included to show the efficiency of the proposed nonlinear scheme.

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Authors and Affiliations

  1. Mechanics and Automation Engineering, Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Quan-Fang Wang

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Correspondence to Quan-Fang Wang.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 70, Differential Equations and Optimal Control, 2011.

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Wang, QF. Optimal distributed control of nonlinear Cahn–Hilliard systems with computational realization. J Math Sci 177, 440–458 (2011). https://doi.org/10.1007/s10958-011-0470-z

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