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2019 | OriginalPaper | Chapter

Impulsive Relaxation of Continuity Equations and Modeling of Colliding Ensembles

Authors : Maxim Staritsyn, Nikolay Pogodaev

Published in: Optimization and Applications

Publisher: 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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previous chapter The Space-Time Representation for Optimal Impulsive Control Problems with Hysteresis

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Title: Impulsive Relaxation of Continuity Equations and Modeling of Colliding Ensembles
Authors: Maxim Staritsyn
Nikolay Pogodaev
Publisher: Springer International Publishing
Book: Optimization and Applications
Print ISBN: 978-3-030-10933-2

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

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

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