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Continuum Modeling of Biological Network Formation Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Sparse Control of Multiagent Systems

Authors : Mattia Bongini, Massimo Fornasier

Published in: Active Particles, Volume 1

Publisher: Springer International Publishing

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Abstract

In recent years, numerous studies have focused on the mathematical modeling of social dynamics, with self-organization, i.e., the autonomous pattern formation, as the main driving concept. Usually, first- or second-order models are employed to reproduce, at least qualitatively, certain global patterns (such as bird flocking, milling schools of fish, or queue formations in pedestrian flows, just to mention a few). It is, however, common experience that self-organization does not always spontaneously occur in a society. In this review chapter, we aim to describe the limitations of decentralized controls in restoring certain desired configurations and to address the question of whether it is possible to externally and parsimoniously influence the dynamics to reach a given outcome. More specifically, we address the issue of finding the sparsest control strategy for finite agent-based models in order to lead the dynamics optimally toward a desired pattern.

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previous chapter Variational Mean Field Games
next chapter A Kinetic Theory Approach to the Modeling of Complex Living Systems
Footnotes
1
Given a real \(N\times N\) matrix \(A = (a_{ij})_{i,j = 1}^N\) and \(v\in {\mathbb R}^{dN}\), we denote by Av the action of A on \({\mathbb R}^{dN}\) by mapping v to \((a_{i1}v_{1} + \cdots + a_{iN}v_{N})_{i=1}^N\). Given a nonnegative symmetric \(N \times N\) matrix \(A = (a_{ij})_{i,j = 1}^N\), the Laplacian L of A is defined by \(L = D - A\), with \(D = \mathrm {diag} (d_{1}, \ldots , d_{N})\) and \(d_{k} = \sum _{j=1}^{N} a_{kj}\).
 
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Metadata
Title
Sparse Control of Multiagent Systems
Authors
Mattia Bongini
Massimo Fornasier
Copyright Year
2017
Book
Active Particles, Volume 1

Print ISBN: 978-3-319-49994-9

Electronic ISBN: 978-3-319-49996-3

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-49996-3_5

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