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.
Highlights
The study of complex networks is of great importance for the scientific community due to the interconnected nature of the modern world and the wide range of meaningful applications [1,2,3,4]
In [7], for example, a complex network with different chaotic node dynamics was controlled using inverse optimal control and V-stability; the latter changes the problem to a linear algebra one
A previous study was undertaken where we examined the impulsive control of discrete-time complex dynamical networks with an experimental approach rather than an analytical one [12]
Summary
The study of complex networks is of great importance for the scientific community due to the interconnected nature of the modern world and the wide range of meaningful applications [1,2,3,4]. In [7], for example, a complex network with different chaotic node dynamics was controlled using inverse optimal control and V-stability; the latter changes the problem to a linear algebra one This change performs the gain selection process more . Neural networks have a wide range of applications depending on their configuration [13], and one of them is the learning control approach that recreates the dynamics of nonlinear systems using the corresponding measurements as the neural identifiers [14,15] The output of these neural identifiers can be used to compute the desired control input. The aim of this research is pin control of a discrete-time complex network with different node dynamics and an impulsive control input, introducing a linear algebra approach for easy gain selection, which is the main contribution of this paper. Preliminaries we describe the mathematical tools used for analysis and simulations
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