Functional differential games with nonatomic difference operator - Vlasenko, L. A.; Rutkas, A. G.; Chikrii, A. O. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.9 We study a differential game of approach in a system whose dynamics is described by 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.