On the unimprovability of full-memory strategies in problems of guaranteed result optimization

A problem of guaranteed result optimization is considered for a control system described by an ordinary differential equation and for a performance functional that depends continuously on the trajectory of the system. The values of the control and of the disturbance satisfy compact geometric constraints. It is also assumed that the realization of the disturbance is subject to an unknown functional constraint from a given set of constraints that are compact in a Lebesgue space.
It is shown that the optimal guaranteed result in the class of full-memory strategies in this problem coincides with the value of the optimal guaranteed result in the class of quasi-strategies.