Mylvaganam, T., Bauso, D. and Astolfi, A. (2015) Mean-field games and two-point boundary value problems. In: Proceedings of the IEEE Conference on Decision and Control. 53rd IEEE Conference on Decision and Control, December 15-17, 2014, Los Angeles, CA, USA. IEEE , 2722 - 2727.
Abstract
© 2014 IEEE. A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equations, with two-point boundary value conditions, can be solved in place of the more complicated partial differential equations associated with the problem. The theory is illustrated by a numerical example.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 29 Jan 2016 16:32 |
Last Modified: | 29 Jan 2016 16:32 |
Published Version: | http://dx.doi.org/10.1109/CDC.2014.7039806 |
Status: | Published |
Publisher: | IEEE |
Refereed: | Yes |
Identification Number: | 10.1109/CDC.2014.7039806 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89656 |