Functional differential games with nonatomic difference operator - Vlasenko, L. A.; Rutkas, A. G.; Chikrii, A. O. (Ukrains’kyi Matematychnyi Zhurnal, 2022)
UDC 517.9We 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.