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

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.