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Impulsive Pinning Control of Discrete-Time Complex Networks with Time-Varying Connections

Author

Listed:
  • Daniel Ríos-Rivera

    (Departamento de Ciencias Computacionales, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Guadalajara 44430, Mexico)

  • Jorge D. Rios

    (Departamento de Innovación Basada en la Información y el Conocimiento, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Guadalajara 44430, Mexico)

  • Oscar D. Sanchez

    (Departamento de Ciencias Computacionales, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Guadalajara 44430, Mexico)

  • Alma Y. Alanis

    (Departamento de Innovación Basada en la Información y el Conocimiento, Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara, Guadalajara 44430, Mexico)

Abstract

Complex dynamical networks with time-varying connections have characteristics that allow a better representation of real-world complex systems, especially interest in their not static behavior and topology. Their applications reach areas such as communication systems, electrical systems, medicine, robotic, and more. Both continuous and discrete-time complex dynamical networks and the pinning control technique have been studied. However, even with interest in the research on complex networks combining characteristics of discrete-time, time-varying connections, pinning control, and impulsive control, there are few studies reported in the literature. There are some previous studies dealing with impulsively pin-controlling a discrete-time complex network. Nevertheless, they neglect to deal with time-varying connections; they deal with these systems by experimentally using continuous-time methods or linearizing the node dynamics. In this manner, this paper presents a control scheme that not only deals with pin control on discrete-time complex networks but also includes time-varying connections. This paper proposes an impulsive pin control to a zero state using passivity degrees considering a discrete-time complex network with undirected, linear, and diffusive couplings. Additionally, a corresponding mathematical analysis, which allows the representation of the dynamics as a set of symmetric matrices, is presented. With this, certain kinds of time-varying connections can be integrated into the analysis. Moreover, a particular criterion for selecting nodes to pin is also presented. The behavior of the controller for the non-varying and time-varying coupling cases is shown via numeric simulations.

Suggested Citation

  • Daniel Ríos-Rivera & Jorge D. Rios & Oscar D. Sanchez & Alma Y. Alanis, 2022. "Impulsive Pinning Control of Discrete-Time Complex Networks with Time-Varying Connections," Mathematics, MDPI, vol. 10(21), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4051-:d:959586
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    References listed on IDEAS

    as
    1. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    2. Qi, Guoyuan & Chen, Guanrong & Du, Shengzhi & Chen, Zengqiang & Yuan, Zhuzhi, 2005. "Analysis of a new chaotic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 295-308.
    3. Daniel Ríos-Rivera & Alma Y. Alanis & Edgar N. Sanchez, 2020. "Neural-Impulsive Pinning Control for Complex Networks Based on V-Stability," Mathematics, MDPI, vol. 8(9), pages 1-20, August.
    4. Youjian Zhang & Wenjun Yan & Qiang Yang, 2014. "Synchronization Control of Time-Varying Complex Dynamic Network with Nonidentical Nodes and Coupling Time-Delay," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-8, May.
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