Parameters identification and adaptive tracking control of uncertain complex-variable chaotic systems with complex parameters

  • Fangfang ZhangEmail author
  • Kai Sun
  • Yawen Chen
  • Haibo Zhang
  • Cuimei Jiang
Original Paper


As for chaotic nonlinear systems with real parameters, many studies about tracking control have been carried out using fixed control strength. However, tracking control for complex-variable chaotic systems (CVCSs) including complex parameters has not been investigated so far, even though CVCSs have potential applications in various important fields. We present the tracking control method and the parameter identification procedure aiming at CVCSs with complex parameters. Firstly, we propose an adaptive tracking controller between two arbitrary bounded CVCSs, in which dynamic control strength and convergence factors are adopted to augment the adaptivity of the controller and adjust the rapidity of convergence. Secondly, according to persistent excitation and linear independence (LI), we derive the necessary conditions and sufficient conditions separately that uncertain complex parameters converge to the real values, and we extend LI from real functions to complex-variable functions. Then, we present a scheme to ensure the convergence of all uncertain parameters to the real values. We verify the proposed methods through simulations including both interference and random noise. The simulation outcomes exhibit the robustness and validity of our approaches.


Tracking control Parameter identification Chaotic system Linear independence 



This work is partially supported by National Nature Science Foundation of China (Nos. 61603203, 61773010), Nature Science Foundation of Shandong Province (No. ZR2017MF064), Scientific Research Plan of Universities in Shandong Province (J18KA352) and Doctor Project of Qilu University of Technology (No. 0412048416).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering and AutomationQilu University of Technology (Shandong Academy of Sciences)JinanChina
  2. 2.Department of Computer ScienceUniversity of OtagoDunedinNew Zealand
  3. 3.School of ScienceQilu University of Technology (Shandong Academy of Sciences)JinanChina

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