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

Ricardo Aguilar-López, Pablo A. López-Pérez (), Gerardo Lara-Cisneros () and Ricardo Femat ()
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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

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 04, 1-13

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.

Keywords: BEC system; stochastic system; nonlinear control design (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0129183116500406

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