Nonlinear Dynamics

, Volume 95, Issue 2, pp 1221–1243 | Cite as

Secure communication on fractional-order chaotic systems via adaptive sliding mode control with teaching–learning–feedback-based optimization

  • Rui-Guo Li
  • Huai-Ning WuEmail author
Original Paper


Due to the significance of secure communication, we do a research about this problem based on fractional-order chaotic systems, where a communication scheme is presented for encryption and decryption of the signal. Through applying Lyapunov stability theory and property of fractional calculus, an adaptive sliding mode controller is designed to achieve the synchronization phase between encryption system with encryption source and decryption system, which offers a tool to the decryption process. To improve the precision and speed of the decryption, we further put forward an optimization strategy for some parameters of the developed controller based on root mean square error of certain variable as a performance indicator. Meanwhile, as an improved teaching–learning-based optimization algorithm, teaching–learning–feedback-based optimization (TLFBO) algorithm is proposed to optimize the parameters more excellently. Subsequently, the simulation experiments, which contain performance test for TLFBO algorithm and secure communication of the signal, are, respectively, conducted on the benchmark functions as well as fractional-order Lorenz system with encryption source and fractional-order Lü system. At last, the experiment results illustrate the feasibility and practicability of the provided method by comparing with some other ones.


Fractional-order chaotic systems Adaptive sliding mode control Optimization strategy Teaching–learning–feedback-based optimization (TLFBO) algorithm Secure communication 



This work is supported by the National Natural Science Foundation of China (NNSFC) (No. 61522302). In addition, the authors would like to thank the editor and reviewers for their valuable suggestions on improving the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that this research complies with ethical standards, as well as there is no conflict of interests regarding the publication of this manuscript.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical EngineeringBeihang University (Beijing University of Aeronautics and Astronautics)BeijingChina

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