Optimization of the process of axisymmetric vibrations of a circular ring
DOI:
https://doi.org/10.15407/dopovidi2016.07.033Keywords:
optimal control problem, quadratic functional, method of Lagrange multipliers, necessary conditions of optimality, axisymmetric vibrations of a circular ring, system of integro-differential Riccati equationsAbstract
The article discusses the linear-quadratic optimal control problem of axisymmetric vibrations of a circular ring. The urgency of this task arises no doubt, because such problems were mainly investigated in a rectangular Cartesian coordinate system. The author suggestes to use the polar coordinates. Using the method of Lagrange multipliers, the necessary optimality conditions are obtained. The uniqueness of optimal control is proved. We obtain a system of integro-differential Riccati equations and additional conditions for it. The solution of this system makes it possible to write down the formula for calculating the optimal control.
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