Functional differential games with nonatomic difference operator

• Date: 2022
• Main Authors: Vlasenko, L. A., Rutkas, A. G., Chikrii, A. O., Власенко, Л. A., Руткас, А. Г., Чикрій, А. О., Руткас, Анатолий, Чикрий, Аркадий
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6895
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.9 We study a differential game of approach in a system whose dynamics is describedby a linear functional differential equation. The coefficients of the equation are closed linear operators on Hilbert spaces. The operator multiplying the state derivative at the current time is generally non-invertible. The main assumption is a restriction imposed on the characteristic operator pencil of the equation on a ray of real the positive semi-axis. Solutions of the equation are represented with the help of a formula of variation of constants where the delay effect is taken into account by summing shift type operators. To obtain conditions for the approach of the system dynamic vector to a cylindrical terminal set, we use constraints on support functionals of two sets defined by the behavior of pursuer and evader.The paper contains an example to illustrate the differential game in a pseudoparabolic system described by a partial functional differential equation.