{"id":{"repo_id":"wustl","oai_identifier":"oai:openscholarship.wustl.edu:eng_etds-1530"},"canonical_url":"https://search.dev.ndltd.org/etd/wustl/oai:openscholarship.wustl.edu:eng_etds-1530","repository":{"repo_id":"wustl","name":"Washington University in St. Louis","base_url":"https://openscholarship.wustl.edu/do/oai/"},"display":{"title":"Geometric Control of Ensemble Systems","abstract":"Robust and sensorless manipulation of large populations of dynamical systems is prevalent in numerous research areas of science and engineering. Prominent examples range from excitations of spin ensembles in nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI), and desynchronization of neuron ensembles for the treatment of neurological disorders, to approximate steering of robot swarm under bounded model perturbation. However, investigating fundamental properties of such ensemble systems remains a significant challenge, as it is beyond the scope of classical control theory. In this thesis, we study fundamental control problems associated with ensemble systems, including controllability analysis and control input design. In particular, we introduce the notion of ensemble controllability for parameterized populations of control systems and then focus on the investigation of ensemble controllability for linear and bilinear populations. Specifically, we exploit techniques from functional analysis, differential geometry, Lie theory, and symmetric group theory to establish necessary and sufficient conditions for ensemble controllability of linear and bilinear systems. Furthermore, such controllability analyses also inspire the design of control inputs for ensemble systems. In particular, we present a systematic method to construct optimal selective pulses for spin ensembles in MRI and also devise control laws to create synchronization patterns for noisy oscillatory networks.</p>","abstract_html":"Robust and sensorless manipulation of large populations of dynamical systems is prevalent in numerous research areas of science and engineering. Prominent examples range from excitations of spin ensembles in nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI), and desynchronization of neuron ensembles for the treatment of neurological disorders, to approximate steering of robot swarm under bounded model perturbation. However, investigating fundamental properties of such ensemble systems remains a significant challenge, as it is beyond the scope of classical control theory. In this thesis, we study fundamental control problems associated with ensemble systems, including controllability analysis and control input design. In particular, we introduce the notion of ensemble controllability for parameterized populations of control systems and then focus on the investigation of ensemble controllability for linear and bilinear populations. Specifically, we exploit techniques from functional analysis, differential geometry, Lie theory, and symmetric group theory to establish necessary and sufficient conditions for ensemble controllability of linear and bilinear systems. Furthermore, such controllability analyses also inspire the design of control inputs for ensemble systems. In particular, we present a systematic method to construct optimal selective pulses for spin ensembles in MRI and also devise control laws to create synchronization patterns for noisy oscillatory networks.&lt;/p&gt;","abstract_has_math":false,"creators":["Zhang, Wei"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Electrical & Systems Engineering","degree_department":null,"school":null,"contributors":["Jr-Shin Li","Heinz Schaettler, Shen Zeng, Renato Feres, ShiNung Ching,"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-08-15T07:00:00Z","date_published":"2019-08-15T07:00:00Z","updated_at":"2026-07-24T06:13:05Z","subjects":["Ensemble control","Geometric control","Applied Mathematics","Systems Engineering"],"languages":["English (en)"],"rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/eng_etds/485"],"render_values":[{"text":"https://openscholarship.wustl.edu/eng_etds/485","href":"https://openscholarship.wustl.edu/eng_etds/485","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.7936/jted-mm94","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jr-Shin Li","Heinz Schaettler, Shen Zeng, Renato Feres, ShiNung Ching,"]},{"key":"dc:creator","label":"Author","values":["Zhang, Wei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2121-08-29T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Systems Engineering","McKelvey School of Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Ensemble control","Geometric control","Applied Mathematics","Systems Engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]},{"key":"dc:rights","label":"Dc Rights","values":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.7936/jted-mm94","https://openscholarship.wustl.edu/eng_etds/485"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Permanent URL: https://doi.org/10.7936/jted-mm94"]},{"key":"dc:description.abstract","label":"Abstract","values":["Robust and sensorless manipulation of large populations of dynamical systems is prevalent in numerous research areas of science and engineering. Prominent examples range from excitations of spin ensembles in nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI), and desynchronization of neuron ensembles for the treatment of neurological disorders, to approximate steering of robot swarm under bounded model perturbation. However, investigating fundamental properties of such ensemble systems remains a significant challenge, as it is beyond the scope of classical control theory. In this thesis, we study fundamental control problems associated with ensemble systems, including controllability analysis and control input design. In particular, we introduce the notion of ensemble controllability for parameterized populations of control systems and then focus on the investigation of ensemble controllability for linear and bilinear populations. Specifically, we exploit techniques from functional analysis, differential geometry, Lie theory, and symmetric group theory to establish necessary and sufficient conditions for ensemble controllability of linear and bilinear systems. Furthermore, such controllability analyses also inspire the design of control inputs for ensemble systems. In particular, we present a systematic method to construct optimal selective pulses for spin ensembles in MRI and also devise control laws to create synchronization patterns for noisy oscillatory networks.</p>"]},{"key":"dc:title","label":"Title","values":["Geometric Control of Ensemble Systems"]}]}],"canonical_facts":{"dc:contributor":["Jr-Shin Li","Heinz Schaettler, Shen Zeng, Renato Feres, ShiNung Ching,"],"dc:creator":["Zhang, Wei"],"dc:date.available":["2121-08-29T07:00:00Z"],"dc:description":["Permanent URL: https://doi.org/10.7936/jted-mm94"],"dc:description.abstract":["Robust and sensorless manipulation of large populations of dynamical systems is prevalent in numerous research areas of science and engineering. Prominent examples range from excitations of spin ensembles in nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI), and desynchronization of neuron ensembles for the treatment of neurological disorders, to approximate steering of robot swarm under bounded model perturbation. However, investigating fundamental properties of such ensemble systems remains a significant challenge, as it is beyond the scope of classical control theory. In this thesis, we study fundamental control problems associated with ensemble systems, including controllability analysis and control input design. In particular, we introduce the notion of ensemble controllability for parameterized populations of control systems and then focus on the investigation of ensemble controllability for linear and bilinear populations. Specifically, we exploit techniques from functional analysis, differential geometry, Lie theory, and symmetric group theory to establish necessary and sufficient conditions for ensemble controllability of linear and bilinear systems. Furthermore, such controllability analyses also inspire the design of control inputs for ensemble systems. In particular, we present a systematic method to construct optimal selective pulses for spin ensembles in MRI and also devise control laws to create synchronization patterns for noisy oscillatory networks.</p>"],"dc:identifier":["https://doi.org/10.7936/jted-mm94","https://openscholarship.wustl.edu/eng_etds/485"],"dc:language":["English (en)"],"dc:rights":["I have not registered my thesis with the U.S. Copyright Office, and do not intend to."],"dc:subject":["Ensemble control","Geometric control","Applied Mathematics","Systems Engineering"],"dc:title":["Geometric Control of Ensemble Systems"],"thesis:degree_discipline":["Electrical & Systems Engineering","McKelvey School of Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:13:05Z"}