Starting control of vibrations of points of a rectangular membrane
М. ТухтасиновDepartment of Differential Equations and Mathematical Physics, National university of Uzbekistan, Tashkent, 700174, UzbekistanG. M. AbdualimovaDepartment of Differential Equations and Mathematical Physics, National university of Uzbekistan, Tashkent, 700174, Uzbekistan
ABI
Abstract
Abstract The problem of starting control of the vibration of points of a rectangular membrane with fixed boundaries is considered. The concept of implemented functions for these membrane points is introduced. For each function being implemented, valid controls are defined that form the control sets. The structure of the control set is studied. The problem is solved in the game setting, the initial player controls the initial position of the membrane, the second, the initial speed. The criterion of the quality of control is determined by the control standards with which the functional is built. The saddle point of the functional and the equilibrium situation of the game are found.
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