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2019 | OriginalPaper | Buchkapitel

Impulsive Relaxation of Continuity Equations and Modeling of Colliding Ensembles

verfasst von : Maxim Staritsyn, Nikolay Pogodaev

Erschienen in: Optimization and Applications

Verlag: Springer International Publishing

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Abstract

The paper promotes a relatively novel class of multi-agent control systems named “impulsive” continuity equations. Systems of this sort, describing the dynamics of probabilistically distributed “crowd” of homotypic individuals, are intensively studied in the case when the driving vector field is bounded and sufficiently regular. We, instead, consider the case when the vector field is unbounded, namely, affine in a control parameter, which is only integrally constrained. This means that the “crowd” can be influenced by “shock” impacts, i.e., actions of small duration but very high intensity. For such control continuity equations, we design an impulsive relaxation by closing the set of solutions in a suitable coarse topology. The main result presents a constructive form of the relaxed system. A connection of the obtained results to problems of contact dynamics is also discussed along with applications to optimal ensemble control and other promising issues.

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Nächstes Kapitel Analysis of Indicators of High-Technology Production Using Optimization Models, Taking into Account the Shortage of Working Capital

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Titel: Impulsive Relaxation of Continuity Equations and Modeling of Colliding Ensembles
verfasst von: Maxim Staritsyn
Nikolay Pogodaev
Verlag: Springer International Publishing
Buch: Optimization and Applications
Print ISBN: 978-3-030-10933-2

Electronic ISBN: 978-3-030-10934-9

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-10934-9_26

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