ABSTRACT
This chapter devotes to feedback control problems for a dynamical system in a situation of uncertain information about the input disturbances, or in a situation of conflict. Problems of finding controls minmax and maxmin with respect to a given quality index are formalized into a zero-sum differential game of two players. The chapter describes a structure of optimal control strategies and characterizes the optimal ensured result, or, equivalently, the value of the game. The quality indexes estimate motions and control actions over the full period of control. The chapter gives a new classification of differential games according to a type of a quality index and formulate existence theorems for the values and saddle points — pairs of optimal strategies. It notes that optimal strategies can again be constructed as extremal ones, and, for each quality index, accompanying points for the extremal strategies are sought in the spaces of extended variables associated with the relevant sufficient information images.
