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

Saeed KHORASHADIZADEH; Mohammad-Hassan MAJIDI

doi:10.1631/FITEE.1601814

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

Regular Papers | Updated：2022-05-19

- Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications
- 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
- Frontiers of Information Technology & Electronic Engineering Vol. 19, Issue 9, Pages: 1180-1190(2018)
- Affiliations：
  
  Faculty of Electrical and Computer Engineering, University of Birjand, Birjand 97175/376, Iran
- Author bio：
  
  Mohammad-Hassan MAJIDI, E-mail: m.majidi@birjand.ac.ir
- Funds：
- DOI：10.1631/FITEE.1601814
  CLC： TN919;O415
- Received：14 December 2016，
  
  Revised：2018-;9-;9，
  
  Published：2018-09
- Accepted：
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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.
DOI：

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. DOI： 10.1631/FITEE.1601814.

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。

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.

关键词

Keywords

references

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