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Research Papers

A Novel Input–Output Linearization Minimum Sliding Mode Error Feedback Control for Synchronization of FitzHugh–Nagumo Neurons

[+] Author and Article Information
Lu Cao

Assistant Research Fellow
The State Key Laboratory of
Astronautic Dynamics (ADL),
China Xi'an Satellite Control Center,
Xi'an 710043, China
e-mails: caolu_space2015@163.com; lu.cao2@mail.mcgill.ca

Xiaoqian Chen

Professor
College of Aerospace Science and Engineering,
National University of Defense Technology,
Changsha 410073, China
e-mail: chenxiaoqian@nudt.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 28, 2014; final manuscript received November 1, 2015; published online December 11, 2015. Assoc. Editor: Gabor Stepan.

J. Comput. Nonlinear Dynam 11(4), 041011 (Dec 11, 2015) (9 pages) Paper No: CND-14-1061; doi: 10.1115/1.4032074 History: Received February 28, 2014; Revised November 01, 2015

A novel input–output linearization minimum sliding mode error feedback control (I/OMSMEFC) is proposed for the synchronization between two uncoupled FitzHugh–Nagumo (FHN) neurons with different ionic currents and external electrical stimulations. To estimate and offset the system uncertainties and external disturbances, the concept of equivalent control error is introduced, which is the key to utilization of I/OMSMEFC. A cost function is formulated on the basis of the principle of minimum sliding mode covariance constraint; then the equivalent control error is estimated and fed back. It is shown that the proposed I/OMSMEFC can compensate various kinds of system uncertainties and external disturbances. Meanwhile, it can reduce the steady-state error more than the conventional sliding mode control (SMC). In addition, the sliding mode after the I/OMSMEFC will tend to be the ideal SMC, resulting in improved control performance and quantity. Sufficient conditions are given based on the Lyapunov stability theorem and numerical simulations are performed to verify the effectiveness of presented I/OMSMEFC for the chaotic synchronization accurately.

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Figures

Grahic Jump Location
Fig. 1

State trajectory of the FHN neuron

Grahic Jump Location
Fig. 3

Synchronized error states between two synchronized FHN neurons

Grahic Jump Location
Fig. 4

Control input, equivalent control error and the estimate of ξ(t) for two synchronized FHN neurons

Grahic Jump Location
Fig. 2

State trajectories for two synchronized FHN neurons

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