Abstract
The paper deals with obtaining sufficient conditions for existence of an \(\varepsilon \)-equilibrium in the sense of piecewise program strategies in zero-sum games associated with a time-varying nonlinear controlled differential equation in a Banach space and a cost functional of a sufficiently general form. The concept of piecewise program strategies in such a game is defined on the base of a concept of Volterra chain for the operator on the right-hand side in the corresponding integral equation controlled by the opponent players and according to a given partition of the time interval. As an example we consider the game associated with a nonlinear pseudoparabolic partial differential equation governing the evolution of electric field in a semiconductor.
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Translated by V. Potapchouck
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Chernov, A.V. Differential Games in a Banach Space on a Fixed Chain. Autom Remote Control 82, 2006–2023 (2021). https://doi.org/10.1134/S0005117921110151
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DOI: https://doi.org/10.1134/S0005117921110151