Document Type

Article

Publication Date

2023

DOI

10.1007/s10208-022-09560-0

Publication Title

Foundations of Computational Mathematics

Volume

23

Issue

3

Pages

803-832

Abstract

Formal power series products appear in nonlinear control theory when systems modeled by Chen–Fliess series are interconnected to form new systems. In fields like adaptive control and learning systems, the coefficients of these formal power series are estimated sequentially with real-time data. The main goal is to prove the continuity and analyticity of such products with respect to several natural (locally convex) topologies on spaces of locally convergent formal power series in order to establish foundational properties behind these technologies. In addition, it is shown that a transformation group central to describing the output feedback connection is in fact an analytic Lie group in this setting with certain regularity properties.

Rights

This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original authors and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Original Publication Citation

Gray, W. S., Palmstrøm, M., & Schmeding, A. (2023). Continuity of formal power series products in nonlinear control theory. Foundations of Computational Mathematics, 23(3), 803-832. https://doi.org/10.1007/s10208-022-09560-0

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