Far Eastern Mathematical Journal

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The stable synthesis of optimal control in the extremum problem for elliptic equation

A. Yu. Chebotarev

2009, issue 1-2, P. 204–208

Abstract

The optimal control problem for the elliptic equation is considered. The solutions of the elliptic equation are the unstable critical points of corresponding evolution system. The construction of the feedback control provided the stability of optimal state is suggested.

Keywords: optimal control, system of optimality, feedback control, stability of stationary solution

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References

[1] Zh.-L. Lions, Optimal'noe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972, 414 s. [2] Zh.-L. Lions, “Nekotorye voprosy optimal'nogo upravleniya raspredelennymi sistemami”, UMN, 40:4(244) (1985), 55–68. [3] A. V. Fursikov, Optimal'noe upravlenie raspredelennymi sistemami. Teoriya i prilozheniya, Nauchnaya kniga, Novosibirsk, 1999, 350 s. [4] A. V. Fursikov, “Stabiliziruemost' kvazilinejnogo parabolicheskogo uravneniya s pomoshh'yu granichnogo upravleniya s obratnoj svyaz'yu”, Matematicheskij sbornik, 192:4 (2001), 115–160.

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