This paper deals with the optimal feedback control problem for the modified Kelvin-Voigt model. The considered model describes the motion of weakly concentrated aqueous polymer solutions. In our case, the control function (the external force) depends on the velocity of the fluid. In such a way, the control is not selected from a finite set of available controls, but belongs to the image of some multi-valued map. The solution for the control problem of fluid motion is a pair: the velocity of the fluid and the control (the density of external forces). Since there can be many such pairs, the concept of optimal solution naturally arises, which gives a minimum to specified cost functional. For the considered optimal feedback control problem the existence theorem on weak solution is proved.

本文讨论了改进的Kelvin-Voigt模型的最优反馈控制问题。所考虑的模型描述了弱浓缩聚合物水溶液的运动。在我们的情况下，控制功能（外力）取决于流体的速度。这样，控件不是从一组有限的可用控件中选择的，而是属于某些多值映射的图像。流体运动的控制问题的解决方案是一对：流体的速度和控制（外力的密度）。由于可以有许多这样的对，因此自然会产生最佳解决方案的概念，这会使指定的成本函数降至最低。对于考虑的最优反馈控制问题，证明了弱解的存在性定理。