Matching Items (4)
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- All Subjects: Dynamical Systems
- All Subjects: Mathematical Modeling
- Creators: Armbruster, Dieter
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
The Kuramoto model is an archetypal model for studying synchronization in groups
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
of nonidentical oscillators where oscillators are imbued with their own frequency and
coupled with other oscillators though a network of interactions. As the coupling
strength increases, there is a bifurcation to complete synchronization where all oscillators
move with the same frequency and show a collective rhythm. Kuramoto-like
dynamics are considered a relevant model for instabilities of the AC-power grid which
operates in synchrony under standard conditions but exhibits, in a state of failure,
segmentation of the grid into desynchronized clusters.
In this dissertation the minimum coupling strength required to ensure total frequency
synchronization in a Kuramoto system, called the critical coupling, is investigated.
For coupling strength below the critical coupling, clusters of oscillators form
where oscillators within a cluster are on average oscillating with the same long-term
frequency. A unified order parameter based approach is developed to create approximations
of the critical coupling. Some of the new approximations provide strict lower
bounds for the critical coupling. In addition, these approximations allow for predictions
of the partially synchronized clusters that emerge in the bifurcation from the
synchronized state.
Merging the order parameter approach with graph theoretical concepts leads to a
characterization of this bifurcation as a weighted graph partitioning problem on an
arbitrary networks which then leads to an optimization problem that can efficiently
estimate the partially synchronized clusters. Numerical experiments on random Kuramoto
systems show the high accuracy of these methods. An interpretation of the
methods in the context of power systems is provided.
ContributorsGilg, Brady (Author) / Armbruster, Dieter (Thesis advisor) / Mittelmann, Hans (Committee member) / Scaglione, Anna (Committee member) / Strogatz, Steven (Committee member) / Welfert, Bruno (Committee member) / Arizona State University (Publisher)
Created2018
Description
Pogonomyrmex californicus (a species of harvester ant) colonies typically have anywhere from one to five queens. A queen can control the ratio of female to male offspring she produces, field research indicating that this ratio is genetically hardwired and does not change over time relative to other queens. Further, a queen has an individual reproductive advantage if she has a small reproductive ratio. A colony, however, has a reproductive advantage if it has queens with large ratios, as these queens produce many female workers to further colony success. We have developed an agent-based model to analyze the "cheating" phenotype observed in field research, in which queens extend their lifespans by producing disproportionately many male offspring. The model generates phenotypes and simulates years of reproductive cycles. The results allow us to examine the surviving phenotypes and determine conditions under which a cheating phenotype has an evolutionary advantage. Conditions generating a bimodal steady state solution would indicate a cheating phenotype's ability to invade a cooperative population.
ContributorsEngel, Lauren Marie Agnes (Author) / Armbruster, Dieter (Thesis director) / Fewell, Jennifer (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
DescriptionUnderstanding the evolution of opinions is a delicate task as the dynamics of how one changes their opinion based on their interactions with others are unclear.
ContributorsWeber, Dylan (Author) / Motsch, Sebastien (Thesis advisor) / Lanchier, Nicolas (Committee member) / Platte, Rodrigo (Committee member) / Armbruster, Dieter (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)
Created2021