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- Title
Continuity of Formal Power Series Products in Nonlinear Control Theory.
- Authors
Gray, W. Steven; Palmstrøm, Mathias; Schmeding, Alexander
- 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.
- Subjects
NONLINEAR control theory; POWER series; ADAPTIVE control systems; LIE groups; TRANSFORMATION groups
- Publication
Foundations of Computational Mathematics, 2023, Vol 23, Issue 3, p803
- ISSN
1615-3375
- Publication type
Article
- DOI
10.1007/s10208-022-09560-0