Symmetry, Integrability and Geometry: Methods and Applications
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.
Original Publication Citation
Gray, W. S. (2022). Entropy of generating series for nonlinear input-output systems and their interconnections. Symmetry, Integrability and Geometry: Methods and Applications, 18, 1-15, Article 82. https://doi.org/10.3842/SIGMA.2022.082
Gray, W. Steven, "Entropy of Generating Series for Nonlinear Input-Output Systems and their Interconnections" (2022). Electrical & Computer Engineering Faculty Publications. 343.