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Mathematical Methods to Find Optimal Control of Oscillations of a Hinged Beam (Deterministic Case)*

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Cybernetics and Systems Analysis Aims and scope

Abstract

We consider several problem statements for the optimal controlled excitation of oscillations of a hinged beam. Oscillations occur under the influence of several external periodic forces. In the simplest statement, it is assumed that the structure of the beam is homogeneous. In a more complex formulation, inhomogeneities (defects) on the beam are allowed. The goal of controlling the oscillations of the beam is to provide a predetermined shape and a predetermined pointwise phase of oscillations in a given frequency range. The problem is to determine the number of forces and their characteristics (application, amplitude, and phase of oscillations), which provide the desired waveform with a given accuracy. With the help of analytical mathematical methods, the problems in question are reduced to simpler multiextremum problems of minimizing basic functionals, which can be numerically solved using the multifunctional package AORDA PSG.

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References

  1. G. M. Zrazhevsky, “Determination of the optimal parameters of the beam waveform actuation,” Bulletin of Taras Shevchenko National University of Kyiv, Ser. Physics & Matematics, Issue 3 (2013), pp. 138–141. URL: http://nbuv.gov.ua/UJRN/VKNU_fiz_mat_2013_3_34.

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  4. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method for Solid and Structural Mechanics, Butterworth–Heinemann, Oxford (2005).

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  6. AORDA Portfolio Safeguard (PSG). URL: http://www.aorda.com/html/PSG_Help_HTML/index.html?bpoe.htm.

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Authors and Affiliations

  1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    G. Zrazhevsky

  2. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    A. Golodnikov

  3. University of Florida, Gainesville, FL, USA

    S. Uryasev

Authors
  1. G. Zrazhevsky
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  2. A. Golodnikov
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  3. S. Uryasev
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Corresponding author

Correspondence to G. Zrazhevsky.

Additional information

*The study was financially supported by the European Office of Aerospace Research and Development, grant EOARD # 16IOE094/STCU # P695.

Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2019, pp. 145–164.

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Zrazhevsky, G., Golodnikov, A. & Uryasev, S. Mathematical Methods to Find Optimal Control of Oscillations of a Hinged Beam (Deterministic Case)*. Cybern Syst Anal 55, 1009–1026 (2019). https://doi.org/10.1007/s10559-019-00211-x

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  • DOI: https://doi.org/10.1007/s10559-019-00211-x

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