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Mathematics > Optimization and Control

arXiv:1805.02954 (math)
[Submitted on 8 May 2018]

Title:Combinatorial Hopf algebra for interconnected nonlinear systems

Authors:Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard, W. Steven Gray
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Abstract:A detailed expose of the Hopf algebra approach to interconnected input-output systems in nonlinear control theory is presented. The focus is on input-output systems that can been represented in terms of Chen-Fliess functional expansions or Fliess operators. This provides a starting point for a discrete-time version of this theory. In particular, the notion of a discrete-time Fliess operator is given and a class of parallel interconnections is described.
Comments: 43 pages, review article
Subjects: Optimization and Control (math.OC); Combinatorics (math.CO)
Cite as: arXiv:1805.02954 [math.OC]
  (or arXiv:1805.02954v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1805.02954
Journal reference: Springer Proceedings in Mathematics & Statistics, Vol. 267, 2018
Related DOI: https://doi.org/10.1007/978-3-030-01397-4

Submission history

From: Kurusch Ebrahimi-Fard [view email]
[v1] Tue, 8 May 2018 11:47:17 UTC (161 KB)
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