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Adaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations

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  • Jian Liu
  • Kexin Liu
  • Shutang Liu

Abstract

In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n-dimensional time-dependent strict-feedback complex-variable chaotic (hyperchaotic) systems (CVCSs) in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. In detail, we have developed a unified framework for designing the adaptive complex scalar controller to ensure this type of CVCSs asymptotically stable and for selecting complex update laws to estimate unknown complex parameters. In particular, combining Lyapunov functions dependent on complex-valued vectors and back-stepping technique, sufficient criteria on stabilization of CVCSs are derived in the sense of Wirtinger calculus in complex space. Finally, numerical simulation is presented to validate our theoretical results.

Suggested Citation

  • Jian Liu & Kexin Liu & Shutang Liu, 2017. "Adaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-16, May.
    • Handle: RePEc:plo:pone00:0175730
    DOI: 10.1371/journal.pone.0175730
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    References listed on IDEAS

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    1. Jian Liu & Shutang Liu & Fangfang Zhang, 2014. "A Novel Four-Wing Hyperchaotic Complex System and Its Complex Modified Hybrid Projective Synchronization with Different Dimensions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-16, June.
    2. M. Mahmoud, Gamal & A. Mohamed, Ahmed & A. Aly, Shaban, 2001. "Strange attractors and chaos control in periodically forced complex Duffing's oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 292(1), pages 193-206.
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