Combinatorial Hopf algebra for interconnected nonlinear systems

TL;DR

This paper explores a Hopf algebra framework for interconnected nonlinear control systems, focusing on input-output representations via Fliess operators, and extends the theory to discrete-time systems.

Contribution

It introduces a discrete-time version of Fliess operators and describes a class of parallel interconnections within the Hopf algebra approach.

Findings

Developed a discrete-time Fliess operator framework

Described parallel interconnections in the Hopf algebra setting

Extended nonlinear control theory to discrete-time 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.