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

Saeed KHORASHADIZADEH; Mohammad-Hassan MAJIDI

doi:10.1631/FITEE.1601814

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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

常规文章 | Updated：2022-05-19

- 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
- Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications
- 信息与电子工程前沿（英文） 2018年19卷第9期页码：1180-1190
- 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
  中图分类号： TN919;O415
- 收稿：2016-12-14，
  
  修回：2018-;9-;9，
  
  纸质出版：2018-09
- Accepted：
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Saeed KHORASHADIZADEH, Mohammad-Hassan MAJIDI. 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[J]. 信息与电子工程前沿（英文）, 2018,19(9):1180-1190.

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.
Saeed KHORASHADIZADEH, Mohammad-Hassan MAJIDI. 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[J]. 信息与电子工程前沿（英文）, 2018,19(9):1180-1190. DOI： 10.1631/FITEE.1601814.

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

P Bagheri , , , M Shahrokhi , , , H Salarieh . . Adaptive observer- based synchronization of two non-identical chaotic systems with unknown parameters . . J Vibr Contr , , 2015 . . 23 ( ( 3 ): ): 389 - - 399 . . DOI: 10.1177/1077546315580052 http://doi.org/10.1177/1077546315580052 . .

CS Chen . . Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems . . Exp Syst Appl , , 2009 . . 36 ( ( 9 ): ): 11827 - - 11835 . . DOI: 10.1016/j.eswa.2009.04.007 http://doi.org/10.1016/j.eswa.2009.04.007 . .

E Cherrier , , , M Boutayeb , , , J Ragot . . Observers-based synchronization and input recovery for a class of nonlinear chaotic models . . IEEE Trans Circ Syst I , , 2006 . . 53 ( ( 9 ): ): 1977 - - 1988 . . DOI: 10.1109/TCSI.2006.882817 http://doi.org/10.1109/TCSI.2006.882817 . .

MC Chien , , , AC Huang . . Adaptive impedance controller design for flexible-joint electrically-driven robots without computation of the regressor matrix . . Robotica , , 2012 . . 30 ( ( 1 ): ): 133 - - 144 . . DOI: 10.1017/S0263574711000403 http://doi.org/10.1017/S0263574711000403 . .

JY Effa , , , BZ Essimbi , , , JM Ngundam . . Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control . . Nonl Dynam , , 2009 . . 58 ( ( 1-2 ): ): 39 - - 48 . . DOI: 10.1007/s11071-008-9459-7 http://doi.org/10.1007/s11071-008-9459-7 . .

MB Fard , , , S Khorashadizadeh . . Model free robust impedance control of robot manipulators using Fourier series expansion . . AI & Robotics , , 2015 . . p.1 - - 7 . . DOI: 10.1109/RIOS.2015.7270740 http://doi.org/10.1109/RIOS.2015.7270740 . .

MM Fateh , , , S Khorashadizadeh . . Robust control of electrically driven robots by adaptive fuzzy estimation of uncertainty . . Nonl Dynam , , 2012a . . 69 ( ( 3 ): ): 1465 - - 1477 . . DOI: 10.1007/s11071-012-0362-x http://doi.org/10.1007/s11071-012-0362-x . .

MM Fateh , , , S Khorashadizadeh . . Optimal robust voltage control of electrically driven robot manipulators . . Nonl Dynam , , 2012b . . 70 ( ( 2 ): ): 1445 - - 1458 . . DOI: 10.1007/s11071-012-0546-4 http://doi.org/10.1007/s11071-012-0546-4 . .

MM Fateh , , , SM Ahmadi , , , S Khorashadizadeh . . Adaptive RBF network control for robot manipulators . . J AI Data Min , , 2014a . . 2 ( ( 2 ): ): 159 - - 166 . . DOI: 10.22044/jadm.2014.246 http://doi.org/10.22044/jadm.2014.246 . .

MM Fateh , , , S Azargoshasb , , , S Khorashadizadeh . . Model- free discrete control for robot manipulators using a fuzzy estimator . . Int J Comput Math Electr Electron Eng , , 2014b . . 33 ( ( 3 ): ): 1051 - - 1067 . . DOI: 10.1108/COMPEL-05-2013-0185 http://doi.org/10.1108/COMPEL-05-2013-0185 . .

G Grassi , , , S Mascolo . . Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal . . IEEE Trans Circ Syst I , , 1997 . . 44 ( ( 10 ): ): 1011 - - 1014 . . DOI: 10.1109/81.633891 http://doi.org/10.1109/81.633891 . .

G Grassi , , , S Mascolo . . Design of nonlinear observers for hyperchaos synchronization using a scalar signal . . IEEE Int Symp on Circuits and Systems , , 1998 . . p.283 - - 286 . . DOI: 10.1109/ISCAS.1998.704006 http://doi.org/10.1109/ISCAS.1998.704006 . .

JMV Grzybowski , , , M Rafikov , , , JM Balthazar . . Synchronization of the unified chaotic system and application in secure communication . . Commun Nonl Sci Numer Simul , , 2009 . . 14 ( ( 6 ): ): 2793 - - 2806 . . DOI: 10.1016/j.cnsns.2008.09.028 http://doi.org/10.1016/j.cnsns.2008.09.028 . .

MM Gupta , , , L Jin , , , N Homma . . Static and Dynamic Neural Networks: from Fundamentals to Advanced Theory , , : : New York, USA Wiley-IEEE Press , , 2005 . . DOI: 10.1002/0471427950 http://doi.org/10.1002/0471427950 . .

CF Hsu . . Adaptive fuzzy wavelet neural controller design for chaos synchronization . . Expert Syst Appl , , 2011 . . 38 ( ( 8 ): ): 10475 - - 10483 . . DOI: 10.1016/j.eswa.2011.02.092 http://doi.org/10.1016/j.eswa.2011.02.092 . .

AC Huang , , , SC Wu , , , WF Ting . . A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments . . Robotica , , 2006 . . 24 ( ( 2 ): ): 205 - - 210 . . DOI: 10.1017/S0263574705002031 http://doi.org/10.1017/S0263574705002031 . .

A Izadbakhsh , , , S Khorashadizadeh . . Robust task-space control of robot manipulators using differential equations for uncertainty estimation . . Robotica , , 2017 . . 35 ( ( 9 ): ): 1923 - - 1938 . . DOI: 10.1017/S0263574716000588 http://doi.org/10.1017/S0263574716000588 . .

CY Kai , , , AC Huang . . A regressor-free adaptive controller for robot manipulators without Slotine and Li's modification . . Robotica , , 2013 . . 31 ( ( 7 ): ): 105058 DOI: 10.1017/S0263574713000301 http://doi.org/10.1017/S0263574713000301 . .

S Khorashadizadeh , , , MM Fateh . . Adaptive Fourier series- based control of electrically driven robot manipulators . . 3 rd Int Conf on Control, Instrumentation, and Automation , , 2013 . . p.213 - - 218 . . DOI: 10.1109/ICCIAutom.2013.6912837 http://doi.org/10.1109/ICCIAutom.2013.6912837 . .

S Khorashadizadeh , , , MM Fateh . . Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation . . Nonl Dynam , , 2015 . . 79 ( ( 2 ): ): 1151 - - 1161 . . DOI: 10.1007/s11071-014-1730-5 http://doi.org/10.1007/s11071-014-1730-5 . .

S Khorashadizadeh , , , MM Fateh . . Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion . . Robotica , , 2017 . . 35 ( ( 2 ): ): 310 - - 336 . . DOI: 10.1017/S026357471500051X http://doi.org/10.1017/S026357471500051X . .

S Khorashadizadeh , , , M Mahdian . . Voltage tracking control of DC-DC boost converter using brain emotional learning . . 4 th Int Conf on Control, Instrumentation, and Automation , , 2016 . . p.268 - - 272 . . DOI: 10.1109/ICCIAutom.2016.7483172 http://doi.org/10.1109/ICCIAutom.2016.7483172 . .

E Kreyszig . . Advanced Engineering Mathematics . . John Wiley & Sons, Hoboken, USA. , , 2007 . . .

CL Kuo . . Design of a fuzzy sliding-mode synchronization controller for two different chaos systems . . Comput Math Appl , , 2011 . . 61 ( ( 8 ): ): 2090 - - 2095 . . DOI: 10.1016/j.camwa.2010.08.080 http://doi.org/10.1016/j.camwa.2010.08.080 . .

JA Laoye , , , UE Vincent , , , SO Kareem . . Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller . . Chaos Sol Fract , , 2009 . . 39 ( ( 1 ): ): 356 - - 362 . . DOI: 10.1016/j.chaos.2007.04.020 http://doi.org/10.1016/j.chaos.2007.04.020 . .

SM Lee , , , DH Ji , , , JH Park , , , 等 . . $\mathscr{H}$ ∞ synchronization of chaotic systems via dynamic feedback approach . . Phys Lett A , , 2008 . . 372 ( ( 29 ): ): 4905 - - 4912 . . DOI: 10.1016/j.physleta.2008.05.047 http://doi.org/10.1016/j.physleta.2008.05.047 . .

LL Li , , , Y Liu , , , QG Yao . . Robust synchronization of chaotic systems using slidingmode and feedback control . . J Zhejiang Univ-Sci C (Comput & Electron) , , 2014 . . 15 ( ( 3 ): ): 211 - - 222 . . DOI: 10.1631/jzus.C1300266 http://doi.org/10.1631/jzus.C1300266 . .

XR Li , , , LY Zhao , , , GZ Zhao . . Sliding mode control for synchronization of chaotic systems with structure or parameters mismatching . . J Zhejiang Univ-Sci , , 2005 . . 6A ( ( 6 ): ): 571 - - 576 . . DOI: 10.1631/jzus.2005.A0571 http://doi.org/10.1631/jzus.2005.A0571 . .

TL Liao , , , SH Tsai . . Adaptive synchronization of chaotic systems and its application to secure communications . . Chaos Sol Fract , , 2000 . . 11 ( ( 9 ): ): 1387 - - 1396 . . DOI: 10.1016/S0960-0779(99)00051-X http://doi.org/10.1016/S0960-0779(99)00051-X . .

TC Lin , , , FY Huang , , , ZB Du , , , 等 . . Synchronization of fuzzy modeling chaotic time delay memristor-based Chua's circuits with application to secure communication . . Int J Fuzzy Syst , , 2015 . . 17 ( ( 2 ): ): 206 - - 214 . . DOI: 10.1007/s40815-015-0024-5 http://doi.org/10.1007/s40815-015-0024-5 . .

MQ Liu , , , JH Zhang . . Exponential synchronization of general chaotic delayed neural networks via hybrid feedback . . J Zhejiang Univ-Sci A , , 2008 . . 9 ( ( 2 ): ): 262 - - 270 . . DOI: 10.1631/jzus.A071336 http://doi.org/10.1631/jzus.A071336 . .

JA Lu , , , XQ Wu , , , XP Han , , , 等 . . Adaptive feedback synchronization of a unified chaotic system . . Phys Lett A , , 2004 . . 329 ( ( 4-5 ): ): 327 - - 333 . . DOI: 10.1016/j.physleta.2004.07.024 http://doi.org/10.1016/j.physleta.2004.07.024 . .

MR Naseh , , , M Haeri . . Robustness and robust stability of the active sliding mode synchronization . . Chaos Sol Fract , , 2009 . . 39 ( ( 1 ): ): 196 - - 203 . . DOI: 10.1016/j.chaos.2007.01.123 http://doi.org/10.1016/j.chaos.2007.01.123 . .

YA Nijsure , , , G Kaddoum , , , G Gagnon , , , 等 . . Adaptive air-to-ground secure communication system based on ADS-B and wide-area multilateration . . IEEE Trans Veh Technol , , 2016 . . 65 ( ( 5 ): ): 3150 - - 3165 . . DOI: 10.1109/TVT.2015.2438171 http://doi.org/10.1109/TVT.2015.2438171 . .

K Ogata . . Discrete-Time Control Systems (2 nd Ed.) . . Prentice Hall, Englewood Cliffs, USA. , , 1995 . . .

LM Pecora , , , TL Carroll . . Driving systems with chaotic signals . . Phys Rev A , , 1991 . . 44 ( ( 4 ): ): 2374 - - 2383 . . DOI: 10.1103/PhysRevA.44.2374 http://doi.org/10.1103/PhysRevA.44.2374 . .

A Pogromsky , , , H Nijmeijer . . Observer-based robust synchronization of dynamical systems . . Int J Bifurc Chaos , , 1998 . . 8 ( ( 11 ): ): 2243 - - 2254 . . . .

C Shen , , , ZG Shi , , , LX Ran . . Adaptive synchronization of chaotic Colpitts circuits against parameter mismatches and channel distortions . . J Zhejiang Univ-Sci A , , 2006 . . 7 ( ( S2 ): ): 228 - - 236 . . DOI: 10.1631/jzus.2006.AS0228 http://doi.org/10.1631/jzus.2006.AS0228 . .

ZG Shi , , , SH Hong , , , JM Chen , , , 等 . . Particle filter-based synchronization of chaotic Colpitts circuits combating AWGN channel distortion . . Circ Syst Signal Process , , 2008 . . 27 ( ( 6 ): ): 833 - - 845 . . DOI: 10.1007/s00034-008-9062-7 http://doi.org/10.1007/s00034-008-9062-7 . .

ZG Shi , , , SJ Bi , , , HT Zhang , , , 等 . . Improved auxiliary particle filter-based synchronization of chaotic Colpitts circuit and its application to secure communication . . Wirel Commun Mob Comput , , 2013 . . 15 ( ( 10 ): ): 1456 - - 1470 . . DOI: 10.1002/wcm.2446 http://doi.org/10.1002/wcm.2446 . .

JJE Slotine , , , WP Li . . Applied Nonlinear Control . . Prentice- Hall, Englewood Cliffs, USA. , , 1991 . . .

C Wang , , , SS Ge . . Adaptive backstepping control of uncertain Lorenz system . . Int J Bifurc Chaos , , 2001 . . 11 ( ( 4 ): ): 1115 - - 1119 . . DOI: 10.1142/S0218127401002560 http://doi.org/10.1142/S0218127401002560 . .

H Wang , , , JM Ye , , , ZH Miao , , , 等 . . Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication . . Trans Inst Meas Contr , , 2016 . . 40 ( ( 4 ): ): 1177 - - 1187 . . DOI: 10.1177/0142331216678311 http://doi.org/10.1177/0142331216678311 . .

LX Wang . . A Course in Fuzzy Systems and Control . . Prentice-Hall, New York, USA. , , 1997 . . .

Q Wang , , , Y Chen . . Generalized Q-S (lag, anticipated and complete) synchronization in modified Chua's circuit and Hindmarsh-Rose systems . . Appl Math Comput , , 2006 . . 181 ( ( 1 ): ): 48 - - 56 . . DOI: 10.1016/j.amc.2006.01.017 http://doi.org/10.1016/j.amc.2006.01.017 . .

JQ Yang , , , YT Chen , , , FL Zhu . . Associated observer-based synchronization for uncertain chaotic systems subject to channel noise and chaos-based secure communication . . Neurocomputing , , 2015 . . 167 587 - - 595 . . DOI: 10.1016/j.neucom.2015.04.030 http://doi.org/10.1016/j.neucom.2015.04.030 . .

MT Yassen . . Controlling chaos and synchronization for new chaotic system using linear feedback control . . Chaos Sol Fract , , 2005 . . 26 ( ( 3 ): ): 913 - - 920 . . DOI: 10.1016/j.chaos.2005.01.047 http://doi.org/10.1016/j.chaos.2005.01.047 . .

SMH Zadeh , , , S Khorashadizadeh , , , MM Fateh , , , 等 . . Optimal sliding mode control of a robot manipulator under uncertainty using PSO . . Nonl Dynam , , 2016 . . 84 ( ( 4 ): ): 2227 - - 2239 . . DOI: 10.1007/s11071-016-2641-4 http://doi.org/10.1007/s11071-016-2641-4 . .

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