Uncertainty quantification in mean-field-type teams and games

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This article studies uncertainty quantification methodologies in team and strategic decision-making problems of mean-field type. Considering McKean-Vlasov state dynamics are that square integrable over a finite horizon, we use Kosambi-Karhunen-Loeve expansion which is a representation of a stochastic process as an infinite linear combination of orthogonal functions, analogous to a Fourier series representation of a function over a bounded domain. The mean-field-type team and game problems are then transformed into equivalent formulations with series expansions. By identification of coefficients, these mean-field-type problems become interactive systems of deterministic state variables over multiple indexes. We illustrate some situations where these deterministic control and game problems can be handled. In the general setting, approximation methods such as truncature techniques are proposed, and their challenges and limitations are examined.

Original languageEnglish (US)
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4418-4423
Number of pages6
ISBN (Electronic)9781479978861
DOIs
StatePublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Other

Other54th IEEE Conference on Decision and Control, CDC 2015
CountryJapan
CityOsaka
Period12/15/1512/18/15

Fingerprint

Uncertainty Quantification
Mean Field
Game
Orthogonal functions
Fourier series
Random processes
Decision making
Karhunen-Loève Expansion
Orthogonal Functions
Interactive Systems
Finite Horizon
Series Representation
Series Expansion
Approximation Methods
Linear Combination
Stochastic Processes
Bounded Domain
Decision Making
Uncertainty
Methodology

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Hamidou, T. (2015). Uncertainty quantification in mean-field-type teams and games. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 4418-4423). [7402909] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402909

Uncertainty quantification in mean-field-type teams and games. / Hamidou, Tembine.

54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 4418-4423 7402909.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Hamidou, T 2015, Uncertainty quantification in mean-field-type teams and games. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7402909, Institute of Electrical and Electronics Engineers Inc., pp. 4418-4423, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7402909
Hamidou T. Uncertainty quantification in mean-field-type teams and games. In 54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 4418-4423. 7402909 https://doi.org/10.1109/CDC.2015.7402909
Hamidou, Tembine. / Uncertainty quantification in mean-field-type teams and games. 54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 4418-4423
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