POSITIONAL SOLUTION OF A LINEAR OPTIMAL HIERARCHICAL CONTROL PROBLEM

Hierarchical control problems [1, 2] are, as a rule, investigated with in the framework of the theory of differential games [3], though they are intrinsically closer to the classical control problems than the an tagonistic differential games, which have been intensively developing in recent times. The classification of the problems related to the beh avior of dynamic objects under goal-oriented interactions into control and game problems is rather artificial. In this classification, class ical control problems are put at one endpoint, which are characterized by a unified goal for all (possibly, distinct) participants of the co ntrol process. Antagonistic differential games are put at the other en dpoint, in which the participants in one of two groups regard each oth er as opponents or malevolant disturbances. In real conditions, the ma jority of interesting problems occupy an intermediate position, which is determined by the degree and form of the interactions (behavior pri nciples) of the participants with opposing interests. The hierarchical problems among control problems are distinguished by the behavior of the participants. In these problems, the participants do not have a co mmon goal: each pursues his own goal, which is not consistent with the interests of others, but they all observe a strict (hierarchical) act ion in the control process [4]. In this paper, we develop an approach to synthesizing optimal controls for linear hierarchical control probl ems.