A combinatorial Hopf algebra for nonlinear output feedback control systems
Luis A. Duffaut Espinosa, Kurusch Ebrahimi-Fard, W. Steven Gray
TL;DR
This paper introduces a combinatorial Hopf algebra structure based on rooted circle trees, providing a new algebraic framework for analyzing nonlinear feedback control systems using Fliess operators.
Contribution
It defines a novel combinatorial Hopf algebra tailored for nonlinear feedback control, including a cancellation-free formula for its antipode, advancing algebraic methods in control theory.
Findings
Provides a new algebraic structure for nonlinear control systems
Derives a cancellation-free formula for the antipode of the Hopf algebra
Connects combinatorial algebra with Fliess operators in control theory
Abstract
In this work a combinatorial description is provided of a Faa di Bruno type Hopf algebra which naturally appears in the context of Fliess operators in nonlinear feedback control theory. It is a connected graded commutative and non-cocommutative Hopf algebra defined on rooted circle trees. A cancellation free forest formula for its antipode is given.
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