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Combinatorial Hopf Algebras for Interconnected Nonlinear Input-Output Systems with a View Towards Discretization

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 267)

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 be 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 in terms of the quasi-shuffle algebra.

Keywords

Nonlinear control systems Chen–Fliess series Combinatorial Hopf algebras 

AMS Subject Classification

93C10 93B25 16T05 16T30 

Notes

Acknowledgements

The third author was supported by grant SEV-2011-0087 from the Severo Ochoa Excellence Program at the Instituto de Ciencias Matemáticas in Madrid, Spain. This research was also supported by a grant from the BBVA Foundation.

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Authors and Affiliations

  1. 1.Department of Electrical and Biomedical EngineeringUniversity of VermontBurlingtonUSA
  2. 2.Department of Mathematical SciencesNorwegian University of Science and Technology – NTNUTrondheimNorway
  3. 3.Department of Electrical and Computer EngineeringOld Dominion UniversityNorfolkUSA

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