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Full-Text Articles in Physical Sciences and Mathematics
Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis
Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis
Mathematics & Statistics Theses & Dissertations
Volterra integral equations arise in a variety of applications in modern physics and engineering, namely in interactions that contain a memory term. Classical formulations of these problems are largely inflexible when considering non-homogeneous media, which can be problematic when considering long term interactions of real-world applications. The use of fractional derivative and integral terms naturally relax these restrictions in a natural way to consider these problems in a more general setting. One major drawback to the use of fractional derivatives and integrals in modeling is the regularity requirement for functions, where we can no longer assume that functions are as …
Wiener-Fliess Composition Of Formal Power Series: Additive Static Feedback And Shuffle Rational Series, Subbarao Venkatesh Guggilam
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 …