Exact solutions of an inverse optimal stabilization problem for systems with aftereffect of neutral type

Yu. F. Dolgii<sup>ab

a</sup> Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: 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.

Keywords: differential equations with aftereffect of neutral type, optimal stabilization, Riccati equation.

UDC: 517.929

MSC: 34K06, 34K20, 34K30

Received: 06.11.2018
Revised: 08.02.2019
Accepted: 11.02.2019

DOI: 10.21538/0134-4889-2019-25-1-35-44

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