Optimization of the process of axisymmetric vibrations of a circular ring

1Kopets, MM
1National Technical University of Ukraine "Kyiv Polytechnic Institute"
Dopov. Nac. akad. nauk Ukr. 2016, 7:33-38
Section: Information Science and Cybernetics
Language: Ukrainian

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.

Keywords: axisymmetric vibrations of a circular ring, method of Lagrange multipliers, necessary conditions of optimality, optimal control problem, quadratic functional, system of integro-differential Riccati equations
  1. Kopets M. M. Problems of control and infomatics 2015, No 1: 40–51 (in Russian).
  2. Chikrii A. A., Eidel'man S. D. Cybernetics and Systems Analysis, 2012, No 6: 66–99.
  3. Eidel'man S. D., Chikrii A. A. Ukr. mat. J., 2000, 52, No 11: 1566–1583.
  4. Chikrii A. A., Rappoport J. S., Chikrii K. A. Cybernetics and Systems Analysis, 2007, 43, No 5: 719–730. https://doi.org/10.1007/s10559-007-0097-8
  5. Chikrii A. A., Dzyubenko K. J. J. Automation and Information Sciences, 2001, 33, No 5: 62–74.