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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


The Optimal Control Problem for Linear Systems of Non-integer Order with Lumped and Distributed Parameters

Discontinuity, Nonlinearity, and Complexity 4(4) (2015) 429--443 | DOI:10.5890/DNC.2015.11.006

V.A. Kubyshkin; S.S. Postnov

V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Profsoyuznaya str., 65, 117997, Russia

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The optimal control problem for linear dynamic systems of fractional order with lumped and distributed parameters is investigated. This problem is reduced to the classical moment problem. This paper validates the conditions making possible to formulate and resolve the obtained moment problem. Some particular cases of fractional-order systems are discussed. The explicit solutions for the problems of optimal control were obtained in case of systems with lumped parameters. In case of system with distributed parameters an approximate solution analyzed for moment problem. In particular, this paper studies the problem to minimize the norm of control for the assigned time interval and the problem of control with the minimal time of the object transition into the desirable state with the given limitation of the norm of control.


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