Some problems of the theory of linear dynamic nonantagonistic games

Background. The paper discusses some problems of optimal control, namely, the theory of dynamic games when the dynamics of a game is described by the linear integrodifferential and integral vector Volterra equations. The aim is to solve the problems of optimization of distance-type functionals mainly in the sense of Nash. Materials and methods. To solve these problems, the author built a modification of the famous extreme construction of the academician N. N. Krasovskiy developed for ordinary differential systems. The centerpiece of this modification is the new definition of the position of the game for which it is necessary to calculate the total memory to manage stress, that greatly complicates the entire study compared with the case of ordinary differential systems. Results and conclusions. The considered method can be extended to the case of nonlinear integrodifferential and integral systems. The paper presents significantly new results that complement and extend the general theory of dynamic games.