Entropy of Generating Series for Nonlinear Input-Output Systems and Their Interconnections

Abstract

This paper has two main objectives. The first is to introduce a notion of entropy that is well suited for the analysis of nonlinear input-output systems that have a Chen-Fliess series representation. The latter is defined in terms of its generating series over a noncommutative alphabet. The idea is to assign an entropy to a generating series as an element of a graded vector space. The second objective is to describe the entropy of generating series originating from interconnected systems of Chen-Fliess series that arise in the context of control theory. It is shown that one set of interconnections can never increase entropy as defined here, while a second set has the potential to do so. The paper concludes with a brief introduction to an entropy ultrametric space and some open questions.

References in corpus (6)

• Faa di Bruno Hopf Algebra of the Output Feedback Group for Multivariable Fliess Operators
• A combinatorial Hopf algebra for nonlinear output feedback control systems
• SISO Output Affine Feedback Transformation Group and Its Faa di Bruno Hopf Algebra
• The algebraic entropy of classical mechanics
• Generating Series for Networks of Chen-Fliess Series
• Topological Entropy of Formal Languages