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Controlling a class of chaotic quantum system under disturbances and noisy measurements: Application to 1D Bose-Einstein condensate

Author

Listed:
  • Ricardo Aguilar-López

    (Departamento de Biotecnología y Bioingeniería, CINVESTAV-IPN, Av. Instituto Politécnico Nacional, No. 2508, San Pedro Zacatenco, C.P. 07360, D.F., Mexico)

  • Pablo A. López-Pérez

    (Ingeniería en Biociencias Escuela Superior de Apan, Universidad Autónoma del Estado de Hidalgo, Carretera Apan-Calpulalpan, Km.8, Chimalpa Tlalayote s/n, Colonia Chimalpa, C.P. 43900, Apan, Hgo., Mexico)

  • Gerardo Lara-Cisneros

    (División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica, Camino a la Presa San José 2055, Colonia Lomas 4 Sección, C.P. 78216, San Luis Potosí, Mexico)

  • Ricardo Femat

    (División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica, Camino a la Presa San José 2055, Colonia Lomas 4 Sección, C.P. 78216, San Luis Potosí, Mexico)

Abstract

In this paper, a robust nonlinear feedback control scheme with adaptive gain is proposed to control the chaotic behavior in a Bose–Einstein condensate (BEC). The control goal concerns the track or regulation purposes. The BEC system is represented as stochastic ordinary differential equations with measured output perturbed by Gaussian noise, which represents the nature of the quantum systems. The convergence of the BEC control law is analyzed under the frame of the Lyapunov stability theory. Numerical experiments show an adequate performance of the proposed methodology under the required conditions. The results are applicable when the shape of the condensate is sufficiently simple.

Suggested Citation

  • Ricardo Aguilar-López & Pablo A. López-Pérez & Gerardo Lara-Cisneros & Ricardo Femat, 2016. "Controlling a class of chaotic quantum system under disturbances and noisy measurements: Application to 1D Bose-Einstein condensate," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(04), pages 1-13, April.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:04:n:s0129183116500406
    DOI: 10.1142/S0129183116500406
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