基于最小滑模误差反馈控制的FitzHugh-Nagumo神经元同步方法

131 浏览量更新于2024-08-26 1 收藏 668KB PDF 举报

基于 FitzHugh-Nagumo 神经元同步的新型输入输出线性化最小滑模误差反馈控制本文提出了一种新型的输入输出线性化最小滑模误差反馈控制（I/OMS-MEFC）方法，以实现 FitzHugh-Nagumo（FHN）神经元之间的同步。该方法的核心是引入等效控制误差的概念，以估计和抵消系统不确定性和外部扰动。 1. FitzHugh-Nagumo 神经元模型 FitzHugh-Nagumo 模型是一种非线性神经元模型，广泛应用于神经科学和生物物理学研究中。该模型描述了神经元之间的电活动和化学信号传递过程。 2. 输入输出线性化最小滑模误差反馈控制 I/OMS-MEFC 方法基于输入输出线性化理论，旨在实现 FHN 神经元之间的同步。该方法将系统不确定性和外部扰动估计为等效控制误差，然后将其反馈到控制系统中，以调整控制输入和抵消扰动。 3. 等效控制误差等效控制误差是指系统不确定性和外部扰动对控制系统的影响。该概念是 I/OMS-MEFC 方法的核心，通过估计和反馈等效控制误差，实现系统的同步和稳定。 4. 最小滑模_covariance 约束 I/OMS-MEFC 方法基于最小滑模_covariance 约束原理，旨在最小化系统的滑模误差。该方法将滑模误差作为成本函数，通过优化算法来估计等效控制误差。 5. 滑模误差反馈控制滑模误差反馈控制是 I/OMS-MEFC 方法的核心组件。该方法将滑模误差反馈到控制系统中，以调整控制输入和抵消扰动。 6. 应用前景 I/OMS-MEFC 方法具有广泛的应用前景，例如神经网络同步、机器人控制、自动化控制等领域。该方法可以实现系统的同步和稳定，提高系统的鲁棒性和可靠性。 I/OMS-MEFC 方法是一种有效的控制方法，可以实现 FitzHugh-Nagumo 神经元之间的同步。该方法具有广泛的应用前景，具有重要的理论和实践价值。

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

A Novel Input–Output

Linearization Minimum Sliding

Mode Error Feedback Control

for Synchronization of

FitzHugh–Nagumo Neurons

A novel input–output linearization minimum sliding mode error feedback control (I/OMS-

MEFC) is proposed for the synchronization between two uncoupled FitzHugh–Nagumo

(FHN) neurons with different ionic currents and external electrical stimulations. To esti-

mate and offset the system uncertainties and external disturbances, the concept of equiva-

lent 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 con-

ventional sliding mode control (SMC). In addition, the sliding mode after the I/OMS-

MEFC 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 nu-

merical simulations are performed to verify the effectiveness of presented I/OMSMEFC

for the chaotic synchronization accurately. [DOI: 10.1115/1.4032074]

Keywords: synchronization, minimum sliding mode error feed back control, input–output

linearization, FitzHugh–Nagumo (FHN) neuron, different external electrical stimulations

1 Introduction

As we know, the chaotic phenomenon exists widely in nonlin-

ear science ﬁelds, which is a very complex dynamical nonlinear

system and exhibits some characteristic, such as excessive sensi-

tivity to initial conditions, ergodic property in some areas of state

space. That is, small variances in the initial condition can induce

large deviations in system states. Hence, chaotic system has the

widespread application values in many ﬁelds [1–4]. Speciﬁcally,

the chaos synchronization control exhibits tremendous utilization

potential and development, which have received great attentions.

Neural network is one of the complex dynamical networks with

strong backgrounds and various potential real-world applications

[5]. Therefore, it has been a fascinating and important subject of

many research ﬁelds [6]. During the last few years, there emerged

many results about the coupled FHN neuron system, which is usu-

ally utilized to study neural ﬁrings to investigate processing of

information in brain due to the simplicity. The FHN neuron model

was ﬁrst derived as simpliﬁed model of the Hodglein–Huxley neu-

ron model by FitzHugh [7] and Nagumo et al. [8]. There are some

literatures [9,10] that have done many qualitative study of the

FHN model for its nonlinear phenomena. Especially, the synchro-

nization of chaotic neurons under external electric stimulations

(EES) is attracted many interests during the last decade. The pur-

pose of synchronization is to synchronize the states of slave sys-

tem identical or opposite to the states of master system [11]. With

the development of control theory, various control schemes have

been successfully applied to control and synchronization of cha-

otic neurons [12–16]. In Ref. [12], controlling chaos in FHN neu-

ron by the adaptive passive method was introduced.

Synchronization of two uncoupled FHN neurons in EES was

found in Ref. [13] where a nonlinear control technology was

addressed. A novel internal model control method was proposed

for the robust output synchronization [14]. Ambrosio and Aziz

investigated the synchronization and control of coupled

reaction–diffusion FHN systems in Ref. [15]. In addition, Yu

et al. discussed the synchronization of two coupled neurons in the

external electrical stimulation based on adaptive backstepping

SMC method in Ref. [16].

In the past, the chaotic synchronization was discussed under the

assumption of two FHN neurons had the same ionic current and

EES [13,16–18]. In this study, the chaotic synchronized problem

with the existence of system uncertainties and external disturban-

ces between two uncoupled FHN neurons is considered with

different ionic currents and external electrical stimulations. Due

to the existence of system uncertainties and external disturbances,

the SMC is a suitable control methodology. It is well-known that

the SMC is a robust nonlinear feedback control methodology, in

which the structure between the switching surfaces is changed to

achieve the desired performance. The excellent theoretical foun-

dation endows SMC with several advantages, such as rapid

response, low sensitivity to parameter variations and external dis-

turbances, and low computational cost [19]. In Refs. [20,21], a

simple type sliding mode was deﬁned to design the controllers for

synchronization between two identical uniﬁed chaotic systems

where the driven system was assumed to have a single input. Syn-

chronization of two different uncertain chaotic systems with

unknown parameters was realized in Refs. [22,23]. However, for

the practical usage in engineering, the system uncertainties and

external disturbances are always time-varying, which hinders the

control precision of conventional SMC, even to inspire the chat-

tering phenomenon.

With a view to tackle the above limitation, the main goal of this

study is to introduce the I/OMSMEFC to accomplish chaotic syn-

chronization between two uncouple FHN neurons with high

Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the

OURNAL 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.

Journal of Computational and Nonlinear Dynamics JULY 2016, Vol. 11 / 041011-1

2016 by ASME

Downloaded From: http://asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jcnddm/934697/ on 03/27/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

下载后可阅读完整内容，剩余8页未读，立即下载

weixin_38552292

粉丝: 6
资源: 894

基于最小滑模误差反馈控制的FitzHugh-Nagumo神经元同步方法

最新资源