Learning Impulsive Pinning Control of Complex Networks

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.

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

“…Consider the next discrete-time model for a complex network with N nodes, undirected diffusive connections, and impulsive control input [23]:…”

“…In this work, an impulsive pin control of a discrete-time complex network with time varying connections to a zero state is proposed, using passivity degrees defined in [18], which will allow us to approach the problem using a set of symmetric matrices, which later will be useful to introduce a time-varying couplings case. Previously, we have worked on discretetime networks with impulsive control on an experimental level using neural networks [22], developing an algorithm that uses linearization of node self-dynamics [23]. This study expands on the previous work by using passivity degrees defined in [18] instead of the linearized dynamics used before; this facilitates the analysis and application of time-varying connections between nodes.…”

Pinning control of networks: dimensionality reduction through simultaneous block-diagonalization of matrices

“…This motivates the study of a problem in which the nodeto-node coupling among the network nodes is different from the coupling exerted on the pinned nodes. Similar versions of this problem have been previously investigated in [26][27][28][29] using a Lyapunov function (V-stability) which provides a sufficient stability condition. In this paper, we investigate stability using linearization, which provides both necessary and sufficient conditions.…”

Bioinspired Intelligent Algorithms for Optimization, Modeling and Control: Theory and Applications

“…This book contains the successful invited submissions [1][2][3][4][5][6][7][8][9][10][11][12][13] to a Special Issue of Mathematics on the subject area of "Bioinspired Intelligent Algorithms for Optimization, Modeling and Control: Theory and Applications".…”

“…In [10], an optimal operation for reduced energy consumption in an air conditioning system based on a neural controller is considered. In this way, identification is a well-known methodology to obtain an accurate model of a complex dynamic system, and with the obtained model, it is possible to solve difficult nonlinear problems such as those represented by complex networks, as exemplified in [11] with a neural identifier used to design an impulsive pinning control. Another approach for trajectory tracking is presented in [12] for robot manipulators; the proposed methodology is based on biologically inspired metaheuristic optimization algorithms.…”