Date of Award

Fall 2019

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Electrical & Computer Engineering

Committee Director

W. Steven Gray

Committee Member

Luis A. Duffaut

Committee Member

Oscar R. Gonzalez

Committee Member

Dimitrie C. Popescu

Abstract

The feedback interconnection of two systems written in terms of Chen-Fliess series can be described explicitly in terms of the antipode of the output feedback Hopf algebra. At present, there are three known computational approaches to calculating this antipode: the left coproduct method, the right coproduct method, and the derivation method. Each of these algorithms is defined recursively, and thus becomes computationally expensive quite quickly. This motivates the need for a more complete understanding of the algorithmic complexity of these methods, as well as the development of new approaches for determining the Hopf algebra antipode. The main goals of this thesis are to create an implementation in code of the derivation method and compare the computational performance against existing code for the two coproduct methods in Mathematica. Both temporal and spatial complexity are examined empirically, and the main conclusion is that the derivation method yields the best performance.

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DOI

10.25777/v5hd-rg25

ISBN

9781392348925

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