Abstract
We study a differential game of approach in a system whose dynamics is described by a functional differential equation in a Hilbert space. The main assumption on the equation is that the operator multiplying the system state at the current time is the generator of a strongly continuous semigroup of bounded linear operators. Weak solutions of the equation are represented by the variation of constant formula. To obtain solvability conditions for the approach of the system state to a cylindrical terminal set, we use the technique of set-valued mappings and their selections and also constraints on support functionals of sets defined by the behaviors of pursuer and evader. The paper contains an example to illustrate the differential game in a system described by a partial functional differential equation with time delay. In particular, we investigate the heat equation with heat loss and with controlled distributed heat source and leak.
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Chikrii, A.A., Rutkas, A.G., Vlasenko, L.A. (2020). On a Differential Game in a System Described by a Functional Differential Equation. In: Tarasyev, A., Maksimov, V., Filippova, T. (eds) Stability, Control and Differential Games. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-42831-0_6
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