ABSTRACT
This chapter suggests that a general scheme for investigation of conflict-controlled processes, illustrates on various types of functional-differential systems. Employment of the Extremal Targetting Rule, developed in, allows for the game termination in the “first absorption” time in the regular and regularized cases. Similar result was obtained by B. N. Pshenichnyi with the use of the convex analysis technique. On the one hand, this method is the result of extension of the Pontryagin Maximum Principle to the game problems. Positional conflict control by the systems of integral and integro-differential equations was studied in the papers of V. L. Pasikov, G.Ts. Chikrii and K. Volyanskij. Investigations of M. S. Gabrielyan and A. V. Kryazhimskii are devoted to the study of positional conflict counteraction of controlled objects groups. It should be noted that, the Extremal Targetting Rule, as applied to linear systems, is based on using the apparatus of support functions, the notion of Aumann integral of set-valued mapping and the Lyapunov theorem on vector measures.
