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Minimax Terminal Control Problem in Hierarchical Nonlinear Discrete-Time Dynamical System

In this report we consider the nonlinear discrete-time dynamical system consisting of several controlled objects which has two levels of control. One level (or first level) is dominating and the other level (or second level) is subordinate which have different criteria of functioning and are united a priori by determined information and control relations. It is assumed that the motion of each object of this system is described by corresponding nonlinear recurrent vector equation (with a convex vector-values of right part of equation) and depend on both controlled parameters (controls) and non-controlled parameters (noises or simulation errors). The phase states of all objects and all a priori indeterminate parameters of this system are constrained by given finite and convex compact sets in the corresponding Euclidean vector spaces. It is also assumed that the choice of control actions at the second level is subordinate to given conditions which depend on the choice of control actions at
the first level of this control process. The quality of the
control processes of all objects at both control levels in this
system is estimated by corresponding convex functionals which are determine in their terminal (final) phase states and each of them meets the corresponding Lipschiz condition. Under these assumptions, we formulate the minimax program terminal control problem for processes in this two-level hierarchical discrete-time dynamical system and propose the general scheme for its solving.
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