Combinatorial Hopf algebra for interconnected nonlinear systems

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.

43 pages, review article

References in corpus (5)

• Mixable Shuffles, Quasi-shuffles and Hopf Algebras
• Hopf algebras, from basics to applications to renormalization
• Post-Lie algebras and factorization theorems
• Post-Lie Algebras and Isospectral Flows
• Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras

Cited by in corpus (2)

• Planarly branched rough paths and rough differential equations on homogeneous spaces
• Post-symmetric braces and integration of post-Lie algebras