ИСТИНА

Within the range of important applied control problems under present investigation is the one of feedback control of oscillating systems of high dimensions. The given presentation indicates effective schemes for solving such problems under the requirement that control forces should be continuous or smooth functions of time. The system is subjected to unknown but bounded disturbance that may also be in resonance with system. The selected approach is based on constructing weakly invariant set-valued mappings (``Krasovski bridges'') which are further used to design solution strategies through dynamic programming techniques and also to investigate the damping possibilities of the controls under various types of loads and disturbances. The presentation is accompanied by computer animation and numerical simulations based on ellipsoidal toolbox for calculating reach sets. The later allows to tackle problems of realistically high dimensions and solve them in limited time.