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Feedback control for some solutions of the sine-Gordon equation

Author

Listed:
  • Porubov, A.V.
  • Fradkov, A.L.
  • Andrievsky, B.R.

Abstract

Evolution of an initial localized bell-shaped state for the sine-Gordon equation is considered. It is obtained numerically that variation in the parameters of the localized input gives rise to different propagating waves as time goes. The speed gradient feedback control method is employed to achieve unified wave profile weakly dependent on initial conditions. Two speed-gradient like algorithms are developed and compared. It is shown that the algorithm using coefficient at the second spatial derivative term in the sine-Gordon equation allows one to generate the same wave with prescribed energy from different initial states having different energies.

Suggested Citation

  • Porubov, A.V. & Fradkov, A.L. & Andrievsky, B.R., 2015. "Feedback control for some solutions of the sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 17-22.
    • Handle: RePEc:eee:apmaco:v:269:y:2015:i:c:p:17-22
    DOI: 10.1016/j.amc.2015.07.040
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    Cited by:

    1. Chukwuma Ogbonnaya & Chamil Abeykoon & Adel Nasser & Ali Turan, 2021. "A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables," Mathematics, MDPI, vol. 9(9), pages 1-13, April.
    2. Porubov, A.V. & Bondarenkov, R.S. & Bouche, D. & Fradkov, A.L., 2018. "Two-step shock waves propagation for isothermal Euler equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 160-166.

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