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Full-Text Articles in Physical Sciences and Mathematics
Computational Analysis Of Antipode Algorithms For The Output Feedback Hopf Algebra, Lance Berlin
Computational Analysis Of Antipode Algorithms For The Output Feedback Hopf Algebra, Lance Berlin
Electrical & Computer Engineering Theses & Dissertations
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 …
Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman
Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities …
Lead-Acid Battery Model Under Discharge With A Fast Splitting Method, R. Corban Harwood, Valipuram S. Manoranjan, Dean B. Edwards
Lead-Acid Battery Model Under Discharge With A Fast Splitting Method, R. Corban Harwood, Valipuram S. Manoranjan, Dean B. Edwards
Faculty Publications - Department of Mathematics
A mathematical model of a valve-regulated lead-acid battery under discharge is presented as simplified from a standard electrodynamics model. This nonlinear reaction–diffusion model of a battery cell is solved using an operator splitting method to quickly and accurately simulate sulfuric acid concentration. This splitting method incorporates one-sided approximation schemes to preserve continuity over material interfaces encompassing discontinuous parameters. Numerical results are compared with measured data by calculating battery voltage from modeled acid concentration as derived from the Nernst equation.
Krylov Subspaces From Bilinear Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov
Krylov Subspaces From Bilinear Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov
Articles
For efficient simulation of state-of-the-art dynamical systems as arise in all aspects of engineering, the development of reduced-order models is of paramount importance. While linear reduction techniques have received considerable study, increasingly nonlinear model reduction is becoming a significant field of interest. From a circuits and systems viewpoint, systems involving micromachined devices or systems involving mixed technologies necessitate the development of reduced-order nonlinear models. From a control systems viewpoint, the design of controllers for nonlinear systems is greatly facilitated by nonlinear model reduction strategies. To this end, the paper proposes two novel model-reduction strategies for nonlinear systems. The first involves …
Controllability And Local Accessibility—A Normal Form Approach, Wei Kang, Mingqing Xiao, Issa Amadou Tall
Controllability And Local Accessibility—A Normal Form Approach, Wei Kang, Mingqing Xiao, Issa Amadou Tall
Articles and Preprints
Given a system with an uncontrollable linearization at the origin, we study the controllability of the system at equilibria around the origin. If the uncontrollable mode is nonzero, we prove that the system always has other equilibria around the origin. We also prove that these equilibria are linearly controllable provided a coefficient in the normal form is nonzero. Thus, the system is qualitatively changed from being linearly uncontrollable to linearly controllable when the equilibrium point is moved from the origin to a different one. This is called a bifurcation of controllability. As an application of the bifurcation, systems with a …
Nonlinear Equations And Wavelets, Andrei Ludu