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CLC number: TN919; O415

On-line Access: 2018-11-11

Received: 2016-12-14

Revision Accepted: 2017-03-07

Crosschecked: 2018-09-09

Cited: 0

Clicked: 1993

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Saeed Khorashadizadeh

https://orcid.org/0000-0003-0192-3678

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Frontiers of Information Technology & Electronic Engineering  2018 Vol.19 No.9 P.1180-1190

http://doi.org/10.1631/FITEE.1601814


Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications


Author(s):  Saeed Khorashadizadeh, Mohammad-Hassan Majidi

Affiliation(s):  Faculty of Electrical and Computer Engineering, University of Birjand, Birjand 97175/376, Iran

Corresponding email(s):   m.majidi@birjand.ac.ir

Key Words:  Observer-based synchronization, Chaotic systems, Legendre polynomials, Secure communications


Saeed Khorashadizadeh, Mohammad-Hassan Majidi. Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications[J]. Frontiers of Information Technology & Electronic Engineering, 2018, 19(9): 1180-1190.

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Abstract: 
In this study, a new controller for chaos synchronization is proposed. It consists of a state feedback controller and a robust control term using legendre polynomials to compensate for uncertainties. The truncation error is also considered. Due to the orthogonal functions theorem, legendre polynomials can approximate nonlinear functions with arbitrarily small approximation errors. As a result, they can replace fuzzy systems and neural networks to estimate and compensate for uncertainties in control systems. legendre polynomials have fewer tuning parameters than fuzzy systems and neural networks. Thus, their tuning process is simpler. Similar to the parameters of fuzzy systems, Legendre coefficients are estimated online using the adaptation rule obtained from the stability analysis. It is assumed that the master and slave systems are the Lorenz and Chen chaotic systems, respectively. In secure communication systems, observer-based synchronization is required since only one state variable of the master system is sent through the channel. The use of observer-based synchronization to obtain other state variables is discussed. Simulation results reveal the effectiveness of the proposed approach. A comparison with a fuzzy sliding mode controller shows that the proposed controller provides a superior transient response. The problem of secure communications is explained and the controller performance in secure communications is examined.

利用勒让德多项式同步两种不同的混沌系统及其在安全通信中的应用

摘要:提出一种新的由状态反馈控制器和鲁棒控制项组成的混沌同步控制器,采用勒让德多项式补偿不确定性,还考虑截断错误。由于正交函数定理,勒让德多项式可逼近任意小的近似误差的非线性函数。因此,勒让德多项式可取代模糊系统和神经网络来估计和补偿控制系统中的不确定性。勒让德多项式具有比模糊系统和神经网络更少的调整参数,它的调整过程更为简单。与模糊系统的参数类似,使用从稳定性分析获得的自适应规则在线估计勒让德系数。假设主系统和从系统分别是Lorenz混沌系统和Chen混沌系统。安全通信系统需要基于观测器同步,因为主系统通过信道只发送一个状态变量。讨论了使用基于观测器同步获得其他状态变量的方法。仿真结果表明该方法的有效性。与模糊滑模控制器的比较表明,所提的控制器表现出优异的瞬态响应。此外,解释了安全通信问题,并测试了安全通信中控制器的性能。

关键词:基于观测器同步;混沌系统;勒让德多项式;安全通信

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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