Learning Impulsive Pinning Control of Complex Networks

Alma Y. Alanis, Daniel Ríos-Rivera, Edgar N. Sanchez and Oscar D. Sanchez
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Alma Y. Alanis: Computer Sciences Department, Universidad de Guadalajara, Guadalajara 44430, Mexico
Daniel Ríos-Rivera: Computer Sciences Department, Universidad de Guadalajara, Guadalajara 44430, Mexico
Edgar N. Sanchez: Electrical Engineering Department, CINVESTAV, Unidad Guadalajara, Zapopan 45017, Mexico
Oscar D. Sanchez: Computer Sciences Department, Universidad de Guadalajara, Guadalajara 44430, Mexico

Mathematics, 2021, vol. 9, issue 19, 1-9

Abstract: In this paper, we present an impulsive pinning control algorithm for discrete-time complex networks with different node dynamics, using a linear algebra approach and a neural network as an identifier, to synthesize a learning control law. The model of the complex network used in the analysis has unknown node self-dynamics, linear connections between nodes, where the impulsive dynamics add feedback control input only to the pinned nodes. The proposed controller consists of the linearization for the node dynamics and a reorder of the resulting quadratic Lyapunov function using the Rayleigh quotient. The learning part of the control is done with a discrete-time recurrent high order neural network used for identification of the pinned nodes, which is trained using an extended Kalman filter algorithm. A numerical simulation is included in order to illustrate the behavior of the system under the developed controller. For this simulation, a 20-node complex network with 5 different node dynamics is used. The node dynamics consists of discretized versions of well-known continuous chaotic attractors.

Keywords: complex networks; discrete-time impulsive systems; impulsive control; neural networks (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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