On the Model Motions in Control Problem with Functional Constraints on Disturbances

A control problem for a system described by an ordinary differential equation is considered. It is suggested that the values of the control and of disturbance belong compact sets at every instant. It is also assumed that the disturbance meets some additional functional constraints showing the nature of the problem under consideration. The control quality is assessed by the functional continuous in the metrics of uniform convergence over the set of phase paths of the system. As it is previously stated, a strategy with full memory solves the control problem under compact constraints to the disturbance as well as under other functional constraints which are reduced to them. At the same time, the strategies constructed for the cases above are not universal, i.e. they depend on the starting position of the system motion. The question of possibility to solve the control problem with functional constraints in a narrower (classic) set of strategies (positional strategies) remains open. This paper gives the construction of the universal optimal strategy using a model of the control system in the feedback path. The examples that lead to the expansion of the class of solution strategies up to strategies with full memory are also given.