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Physical Sciences and Mathematics Commons

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Theses/Dissertations

Old Dominion University

Mathematics

Nonlinear systems

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Full-Text Articles in Physical Sciences and Mathematics

Wiener-Fliess Composition Of Formal Power Series: Additive Static Feedback And Shuffle Rational Series, Subbarao Venkatesh Guggilam Jul 2021

Wiener-Fliess Composition Of Formal Power Series: Additive Static Feedback And Shuffle Rational Series, Subbarao Venkatesh Guggilam

Electrical & Computer Engineering Theses & Dissertations

The problem statement for this dissertation is two-fold. The first problem considered is when does a Chen-Fliess series in an additive static feedback connection with a formal static map yield a closed-loop system with a Chen-Fliess series expansion? This work proves that such a closed-loop system always has a Chen-Fliess series representation. Furthermore, an algorithm based on the Hopf algebras for the shuffle group and the dynamic output feedback group is designed to compute the generating series of the closed-loop system. It is proved that the additive static feedback connection preserves local convergence and relative degree, but a counterexample shows …


Computational Methods For Nonlinear Systems Analysis With Applications In Mathematics And Engineering, Geoffrey Kenneth Rose Oct 2017

Computational Methods For Nonlinear Systems Analysis With Applications In Mathematics And Engineering, Geoffrey Kenneth Rose

Mechanical & Aerospace Engineering Theses & Dissertations

An investigation into current methods and new approaches for solving systems of nonlinear equations was performed. Nontraditional methods for implementing arc-length type solvers were developed in search of a more robust capability for solving general systems of nonlinear algebraic equations. Processes for construction of parameterized curves representing the many possible solutions to systems of equations versus finding single or point solutions were established. A procedure based on these methods was then developed to identify static equilibrium states for solutions to multi-body-dynamic systems. This methodology provided for a pictorial of the overall solution to a given system, which demonstrated the possibility …