Research Papers

Robust Adaptive Synchronization of Chaotic Systems With Nonsymmetric Input Saturation Constraints

[+] Author and Article Information
Samaneh Mohammadpour

Department of Electrical and
Electronic Engineering,
Shiraz University of Technology,
Modares Boulevard,
P.O. Box 71555-313,
Shiraz 71557-13876, Iran
e-mail: s.mohamadpor@sutech.ac.ir

Tahereh Binazadeh

Department of Electrical and
Electronic Engineering,
Shiraz University of Technology,
Modares Boulevard,
P.O. Box 71555-313,
Shiraz 71557-13876, Iran
e-mail: binazadeh@sutech.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 22, 2016; final manuscript received August 8, 2017; published online October 9, 2017. Assoc. Editor: Katrin Ellermann.

J. Comput. Nonlinear Dynam 13(1), 011005 (Oct 09, 2017) (7 pages) Paper No: CND-16-1574; doi: 10.1115/1.4037672 History: Received November 22, 2016; Revised August 08, 2017

This paper considers the robust synchronization of chaotic systems in the presence of nonsymmetric input saturation constraints. The synchronization happens between two nonlinear master and slave systems in the face of model uncertainties and external disturbances. A new adaptive sliding mode controller is designed in a way that the robust synchronization occurs. In this regard, a theorem is proposed, and according to the Lyapunov approach the adaptation laws are derived, and it is proved that the synchronization error converges to zero despite of the uncertain terms in master and slave systems and nonsymmetric input saturation constraints. Finally, the proposed method is applied on chaotic gyro systems to show its applicability. Computer simulations verify the theoretical results and also show the effective performance of the proposed controller.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Pecora, L. M. , and Carroll, T. L. , 1990, “ Synchronization in Chaotic Systems,” Phys. Rev. Lett., 64(8), pp. 821–824. [CrossRef] [PubMed]
Skinner, J. E. , Molnar, M. , Vybiral, T. , and Mitra, M. , 1992, “ Application of Chaos Theory to Biology and Medicine,” Integr. Physiol. Behav. Sci., 27(1), pp. 39–53. [CrossRef] [PubMed]
Yang, X. , Cao, J. , and Yang, Z. , 2013, “ Synchronization of Coupled Reaction-Diffusion Neural Networks With Time-Varying Delays Via Pinning-Impulsive Controller,” SIAM J. Control Optim., 51(5), pp. 3486–3510. [CrossRef]
Morcillo, J. D. , Burbano, D. , and Angulo, F. , 2016, “ Adaptive Ramp Technique for Controlling Chaos and Subharmonic Oscillations in DC–DC Power Converters,” IEEE Trans. Power Electron., 31(7), pp. 5330–5343. [CrossRef]
Liu, Y. , Li, L. , and Feng, Y. , 2016, “ Finite-Time Synchronization for High-Dimensional Chaotic Systems and Its Application to Secure Communication,” ASME J. Comput. Nonlinear Dyn., 11(5), p. 051028. [CrossRef]
Lu, J. , Kurths, J. , Cao, J. , Mahdavi, N. , and Huang, C. , 2012, “ Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy,” IEEE Trans. Neural Networks Learn. Syst., 23(2), pp. 285–292. [CrossRef]
Cao, L. , and Chen, X. , 2015, “ Input–Output Linearization Minimum Sliding Mode Error Feedback Control for Synchronization of Chaotic System,” Proc. Inst. Mech. Eng., Part I, 229(8), pp. 685–699.
Yang, S. , Li, C. , and Huang, T. , 2016, “ Exponential Stabilization and Synchronization for Fuzzy Model of Memristive Neural Networks by Periodically Intermittent Control,” Neural Networks, 75, pp. 162–172. [CrossRef] [PubMed]
Abbasi, Y. , Moosavian, S. A. A. , and Novinzadeh, A. B. , 2016, “ Formation Control of Aerial Robots Using Virtual Structure and New Fuzzy-Based Self-Tuning Synchronization,” Trans. Inst. Meas. Control, epub.
Singh, A. K. , Yadav, V. K. , and Das, S. , 2017, “ Dual Combination Synchronization of the Fractional Order Complex Chaotic Systems,” ASME J. Comput. Nonlinear Dyn., 12(1), p. 011017. [CrossRef]
Xing-Yuan, W. , and Hao, Z. , 2013, “ Backstepping-Based Lag Synchronization of a Complex Permanent Magnet Synchronous Motor System,” Chin. Phys. B, 22(4), p. 048902. [CrossRef]
Mohammadpour, S. , and Binazadeh, T. , 2017, “ Observer-Based Synchronization of Uncertain Chaotic Systems Subject to Input Saturation,” Trans. Inst. Meas. Control, epub.
Bagheri, P. , Shahrokhi, M. , and Salarieh, H. , 2017, “ Adaptive Observer-Based Synchronization of Two Non-Identical Chaotic Systems With Unknown Parameters,” J. Vib. Control, 23(3), pp. 389–399. [CrossRef]
Luo, R. , and Zeng, Y. , 2016, “ The Control and Synchronization of a Class of Chaotic Systems With Output Variable and External Disturbance,” ASME J. Comput. Nonlinear Dyn., 11(5), p. 051011. [CrossRef]
Aghababa, M. P. , and Aghababa, H. P. , 2012, “ A General Nonlinear Adaptive Control Scheme for Finite-Time Synchronization of Chaotic Systems With Uncertain Parameters and Nonlinear Inputs,” Nonlinear Dyn., 69(4), pp. 1903–1914. [CrossRef]
Aghababa, M. P. , and Aghababa, H. P. , 2014, “ Stabilization of Gyrostat System With Dead-Zone Nonlinearity in Control Input,” J. Vib. Control, 20(15), pp. 2378–2388. [CrossRef]
Wang, N. , Qian, C. , Sun, J. C. , and Liu, Y. C. , 2016, “ Adaptive Robust Finite-Time Trajectory Tracking Control of Fully Actuated Marine Surface Vehicles,” IEEE Trans. Control Syst. Technol., 24(4), pp. 1454–1462. [CrossRef]
Yu, W. , DeLellis, P. , Chen, G. , di Bernardo, M. , and Kurths, J. , 2012, “ Distributed Adaptive Control of Synchronization in Complex Networks,” IEEE Trans. Autom. Control, 57(8), pp. 2153–2158. [CrossRef]
Zhao, Y. P. , He, P. , Saberi Nik, H. , and Ren, J. , 2015, “ Robust Adaptive Synchronization of Uncertain Complex Networks With Multiple Time-Varying Coupled Delays,” Complexity, 20(6), pp. 62–73. [CrossRef]
Kebriaei, H. , and Yazdanpanah, M. J. , 2010, “ Robust Adaptive Synchronization of Different Uncertain Chaotic Systems Subject to Input Nonlinearity,” Commun. Nonlinear Sci. Numer. Simul., 15(2), pp. 430–441. [CrossRef]
Jaramillo-Lopez, F. , Kenne, G. , and Lamnabhi-Lagarrigue, F. , 2017, “ Adaptive Control for a Class of Uncertain Nonlinear Systems: Application to Photovoltaic Control Systems,” IEEE Trans. Autom. Control, 62(1), pp. 393–398. [CrossRef]
Binazadeh, T. , and Bahmani, M. , 2016, “ Robust Time-Varying Output Tracking Control in the Presence of Actuator Saturation,” Trans. Inst. Meas. Control, epub.
Binazadeh, T. , and Bahmani, M. , 2017, “ Design of Robust Controller for a Class of Uncertain Discrete-Time Systems Subject to Actuator Saturation,” IEEE Trans. Autom. Control, 62(3), pp. 1505–1510. [CrossRef]
Hao, L. Y. , and Yang, G. H. , 2013, “ Fault Tolerant Control for a Class of Uncertain Chaotic Systems With Actuator Saturation,” Nonlinear Dyn., 73(4), pp. 2133–2147. [CrossRef]
Gußner, T. , Jost, M. , and Adamy, J. , 2012, “ Controller Design for a Class of Nonlinear Systems With Input Saturation Using Convex Optimization,” Syst. Control Lett., 61(1), pp. 258–265. [CrossRef]
Ran, M. , Wang, Q. , and Dong, C. , 2016, “ Stabilization of a Class of Nonlinear Systems With Actuator Saturation Via Active Disturbance Rejection Control,” Automatica, 63, pp. 302–310. [CrossRef]
Wang, Q. , Ran, M. , and Dong, C. , 2016, “ An Analysis and Design Method for a Class of Nonlinear Systems With Nested Saturations,” Int. J. Control, 89(8), pp. 1711–1724. [CrossRef]
Silva, J. M. , Oliveira, M. Z. , Coutinho, D. , and Tarbouriech, S. , 2014, “ Static Anti‐Windup Design for a Class of Nonlinear Systems,” Int. J. Robust Nonlinear Control, 24(5), pp. 793–810. [CrossRef]
Iqbal, M. , Rehan, M. , Hong, K. S. , and Khaliq, A. , 2015, “ Sector-Condition-Based Results for Adaptive Control and Synchronization of Chaotic Systems Under Input Saturation,” Chaos, Solitons Fractals, 77, pp. 158–169. [CrossRef]
Hu, Q. , 2008, “ Adaptive Output Feedback Sliding-Mode Manoeuvring and Vibration Control of Flexible Spacecraft With Input Saturation,” IET Control Theory Appl., 2(6), pp. 467–478. [CrossRef]
Khalil, H. K. , 2014, Nonlinear Control, Prentice Hall, Upper Saddle River, NJ. [PubMed] [PubMed]
Binazadeh, T. , 2016, “ Finite-Time Tracker Design for Uncertain Nonlinear Fractional-Order Systems,” ASME J. Comput. Nonlinear Dyn., 11(4), p. 041028. [CrossRef]
Chenarani, H. , and Binazadeh, T. , 2017, “ Flexible Structure Control of Unmatched Uncertain Nonlinear Systems Via Passivity-Based Sliding Mode Technique,” Iran. J. Sci. Technol., Trans. Electr. Eng., 41(1), pp. 1–11. [CrossRef]
Binazadeh, T. , and Yousefi, M. , 2017, “ Designing a Cascade-Control Structure Using Fractional-Order Controllers: Time-Delay Fractional-Order Proportional-Derivative Controller and Fractional-Order Sliding-Mode Controller,” J. Eng. Mech., 143(7), p. 04017037. [CrossRef]
Yousefi, M. , and Binazadeh, T. , 2017, “ Delay-Independent Sliding Mode Control of Time-Delay Linear Fractional Order Systems,” Trans. Inst. Meas. Control, epub.
Binazadeh, T. , and Shafiei, M. H. , 2013, “ Output Tracking of Uncertain Fractional-Order Nonlinear Systems Via a Novel Fractional-Order Sliding Mode Approach,” Mechatronics, 23(7), pp. 888–892. [CrossRef]
Behjameh, M. R. , Delavari, H. , and Vali, A. , 2015, “ Global Finite Time Synchronization of Two Nonlinear Chaotic Gyros Using High Order Sliding Mode Control,” J. Appl. Comput. Mech., 1(1), pp. 26–34.
Lei, Y. , Xu, W. , and Zheng, H. , 2005, “ Synchronization of Two Chaotic Nonlinear Gyros Using Active Control,” Phys. Lett. A, 343(1–3), pp. 153–158. [CrossRef]


Grahic Jump Location
Fig. 1

Phase trajectory of the nominal chaotic gyro system

Grahic Jump Location
Fig. 2

Time-responses of synchronization errors without applying the proposed controller

Grahic Jump Location
Fig. 3

Time-responses of state variables of the master and slave systems by applying the proposed controller: (a)x1(t),y1(t) and (b)x2(t),y2(t)

Grahic Jump Location
Fig. 4

Time-response of the sliding surface

Grahic Jump Location
Fig. 5

Time-responses of the synchronization errors with uH=3 and−uL=−4 : (a) by saturated control signal given in Ref. [36] and (b) by the proposed saturated control signal

Grahic Jump Location
Fig. 6

Time-responses of the saturated control signal with uH=3 and−uL=−4 : (a) given controller in Ref. [38] and (b) proposed controller in this paper

Grahic Jump Location
Fig. 7

Time-responses of parameters η(t),λ̂(t), and γ1(t)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In