Date of Award

Summer 8-2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Electrical & Computer Engineering

Program/Concentration

Electrical and Computer Engineering

Committee Director

W. Steven Gray

Committee Member

Luis A. Duffaut Espinosa

Committee Member

Oscar R. Gonzalez

Abstract

In control theory, a Chen-Fliess functional series is a weighted sum of iterated integrals constructed from a given set of input functions. Such series can be used to represent nonlinear input-output systems. In applications, they have been employed to characterize interconnected nonlinear systems, to solve system inversion and tracking problems, and to design predictive and adaptive controllers.

Distributed parameter systems exhibit spatial dependence along with temporal dependence. Such systems are typically represented in terms of partial differential equations. In control theory, there appears to be no existing method for representing the input-output map of a distributed system via a Chen-Fliess functional expansion beyond the previous work of the author, which was restricted to the linear case. The main goal of this dissertation is to present a generalized type of Chen-Fliess series that is parameter dependent. It is capable of describing a broad class of nonlinear input-output maps including but not limited to those for distributed parameter systems. Sufficient conditions are given for series convergence, absolute continuity and differentiability of the output function. The linear case is then further developed in the direction of infinite dimensional state space realizations and applied to a simplified transformer model used in artificial intelligence. The concept is also applied to describe nonrecursive system interconnections, namely parallel and series connections.

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DOI

10.25777/hdwn-5894

ISBN

9798193217152

ORCID

0009-0004-5998-9973

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