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|Exact solutions of an inverse optimal stabilization problem for systems with aftereffect of neutral type
Точные решения обратной задачи оптимальной стабилизации для систем с последействием нейтрального типа
|Dolgii, Yu. F.
|Krasovskii Institute of Mathematics and Mechanics
|Dolgii Yu. F. Exact solutions of an inverse optimal stabilization problem for systems with aftereffect of neutral type / Yu. F. Dolgii. — DOI 10.21538/0134-4889-2019-25-1-35-44 // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2019. — Vol. 25. — Iss. 1. — P. 35-44.
|An optimal stabilization problem is considered for systems of differential equations with aftereffect of neutral type. To simplify the representation of a continuous quadratic functional, an isomorphism of functional spaces is used. The optimal stabilization problem is formulated in a functional space of states with a special metric. A statement of the inverse optimal stabilization problem is presented; this statement is related to the recovery of a system with a given representation of an optimal stabilizing control. Sufficient conditions for the solvability of the inverse problem are obtained, and conditions under which the inverse problem admits analytical solutions are specified. A method for finding exact solutions to this problem is proposed. For systems of differential equations with delay-type aftereffect, exact solutions of the inverse problem were obtained earlier. An example of the exact solution of the inverse problem is given for a system of differential equations with aftereffect of neutral type. © 2019 Krasovskii Institute of Mathematics and Mechanics. All Rights Reserved.
|DIFFERENTIAL EQUATIONS WITH AFTEREFFECT OF NEUTRAL TYPE
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|Научные публикации, проиндексированные в SCOPUS и WoS CC
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