Optimal control over axisymmetric vibrations of a circular membrane
DOI:
https://doi.org/10.15407/dopovidi2015.09.033Keywords:
axisymmetric vibrations of a circular membrane, method of Lagrange multipliers, necessary conditions of optimality, optimal control problem, quadratic functional, system of Riccati equationsAbstract
The article discusses the linear-quadratic problem of optimal control over axisymmetric vibrations of a circular membrane. The statement of the aforementioned task in polar coordinates is suggested. Using the method of Lagrange multipliers, necessary optimality conditions are obtained. The uniqueness of optimal control is proved. A system of integro-differential Riccati equations and additional conditions for it are obtained. The solution of this system makes it possible to write down the formula for calculating the optimal control.
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Kopets M. M. Problems of control and infomatik, 2014, No 1: 12–22 (in Russian).
Kopets M. M. Problems of control and infomatik, 2015, No 1: 40–51.
Chikrii A. A., Eidel'man S. D. Cybernetics and Systems Analysis, 2012, No 6: 66–99 .
Eidel'man S. D., Chikrii A. A. Ukr. mat. zhurn, 2000, 52, No 11: 1566–1583.
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
Chikrii A. A., Dzyubenko K. J. J. of Information Sci, 2001, 33, No 5: 62–74.
Pilipenko Yu. V., Chikrii A. A. Prikl. Matematika i Mechanika, 1993, 57, No 3: 3–14.
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