Parameters identification and adaptive tracking control of uncertain complex-variable chaotic systems with complex parameters
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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.
KeywordsTracking 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).
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Conflict of interest
The authors declare that they have no conflict of interest.
- 4.Zeghlache, H., Mandel, P.: Influence of detuning on the properties of laser equations. J. Opt. Soc. Am. B 2(1), 18–22 (1985)Google Scholar
- 5.Ning, C.Z., Haken, H.: Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hopf bifurcations. Phys. Rev. A 41(7), 3826–3837 (1990)Google Scholar
- 7.Zivkovic, T., Rypdal, K.: Experimental evidence of low-dimensional chaotic convection dynamics in a toroidal magnetized plasma. Phys. Rev. E 77(3), 037401 (2008)Google Scholar
- 23.Zhang, F.F., Liu, S.T.: Full state hybrid projective synchronization and parameters identification for uncertain chaotic (hyperchaotic) complex systems. J. Comput. Nonlinear Dyn. 9(2), 021009 (2014)Google Scholar
- 36.Zhang, F.F., Sun, K., Chen, Y.W., Zhang, H.B.: Adaptive tracking control and parameter identification for uncertain complex-variable chaotic systems. In: The 2018 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2018), July 9–12, 2018, Auckland, New ZealandGoogle Scholar