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

Daniel Ríos-Rivera, Jorge D. Rios, Oscar D. Sanchez and Alma Y. Alanis ()
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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

Mathematics, 2022, vol. 10, issue 21, 1-14

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.

Keywords: complex networks; pinning control; discrete-time systems; impulsive control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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