{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/394049"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/394049","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Performance and stability in decentralised network systems with applications to distributed optimisation and power systems","abstract":"Networked systems underpin numerous modern engineering applications, with the concept of decentralised control playing an essential role in regulating the behaviour of large-scale, heterogeneous architectures. Ensuring that such controllers perform well when interconnected with the rest of the network, while also guaranteeing that the interconnection remains stable, is crucial. This thesis explores these dual problems—performance and stability in decentralised networks—motivated by challenges encountered in contemporary engineering practice. Part I of this thesis concentrates on performance. Many systems, including power and communication networks, benefit from the plug-and-play property, meaning that subsystems can be added or removed without requiring existing controllers to be retuned. Traditionally, plug-and-play functionality is achieved via passivity-based methods, but existing results often omit network-wide performance. To address this issue, we use inverse optimal control to derive local sufficient conditions under which decentralised controllers in a general nonlinear networked system minimise a global, performance-related cost functional, while simultaneously rendering each subsystem passive. We show that this result can be used for control synthesis in linear systems, which is demonstrated with a DC microgrid example. Furthermore, we extend these results to a broad class of nonlinear, nonsmooth primal–dual algorithms used to solve distributed optimisation problems, showing that a set of performance-enhancing augmentations emerges as the optimal solutions to a network-wide cost functional that penalises deviations from optimality during algorithm transients. Part II turns to network stability. Guaranteeing plug-and-play operation through passivity-based methods is often limited in many applications, most notably in AC power systems. Using this example to ground our theoretical developments, we present a decentralised and distributed framework to certify small-signal stability of the grid based entirely on local subsystem analysis. The framework takes the form of quadratic constraints on local subsystems that, when satisfied across the network, collectively imply that the generalised Nyquist criterion holds for the entire grid. We present feasible examples of such conditions for two different subsystem formulations, offering increased flexibility, and demonstrate their application to a microgrid case study. By accommodating non-passive dynamics, our framework offers practical, local tests that lead to stable plug-and-play operation.","abstract_html":"Networked systems underpin numerous modern engineering applications, with the concept of decentralised control playing an essential role in regulating the behaviour of large-scale, heterogeneous architectures. Ensuring that such controllers perform well when interconnected with the rest of the network, while also guaranteeing that the interconnection remains stable, is crucial. This thesis explores these dual problems—performance and stability in decentralised networks—motivated by challenges encountered in contemporary engineering practice. Part I of this thesis concentrates on performance. Many systems, including power and communication networks, benefit from the plug-and-play property, meaning that subsystems can be added or removed without requiring existing controllers to be retuned. Traditionally, plug-and-play functionality is achieved via passivity-based methods, but existing results often omit network-wide performance. To address this issue, we use inverse optimal control to derive local sufficient conditions under which decentralised controllers in a general nonlinear networked system minimise a global, performance-related cost functional, while simultaneously rendering each subsystem passive. We show that this result can be used for control synthesis in linear systems, which is demonstrated with a DC microgrid example. Furthermore, we extend these results to a broad class of nonlinear, nonsmooth primal–dual algorithms used to solve distributed optimisation problems, showing that a set of performance-enhancing augmentations emerges as the optimal solutions to a network-wide cost functional that penalises deviations from optimality during algorithm transients. Part II turns to network stability. Guaranteeing plug-and-play operation through passivity-based methods is often limited in many applications, most notably in AC power systems. Using this example to ground our theoretical developments, we present a decentralised and distributed framework to certify small-signal stability of the grid based entirely on local subsystem analysis. The framework takes the form of quadratic constraints on local subsystems that, when satisfied across the network, collectively imply that the generalised Nyquist criterion holds for the entire grid. We present feasible examples of such conditions for two different subsystem formulations, offering increased flexibility, and demonstrate their application to a microgrid case study. By accommodating non-passive dynamics, our framework offers practical, local tests that lead to stable plug-and-play operation.","abstract_has_math":false,"creators":["Hallinan, Liam"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Lestas, Ioannis"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-08-27","date_published":"2025-08-27","updated_at":"2026-07-22T22:24:28Z","subjects":["control","power systems","optimal control","distributed optimisation","network systems","small-signal stability","inverse optimal control","nyquist techniques"],"languages":["eng"],"rights":[],"rights_urls":["https://www.repository.cam.ac.uk/bitstreams/0bcc2719-049e-4037-af33-7fbda75b6707/download","http://purl.org/NET/rdflicense/allrightsreserved"],"identifier_entries":[{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000202707486"],"render_values":[{"text":"0000-0002-0270-7486","href":"https://orcid.org/0000-0002-0270-7486","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.124143","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Lestas, Ioannis"]},{"key":"dc:contributor.sponsor","label":"Sponsor","values":["UKRI grant EP/T517847/1"]},{"key":"dc:creator","label":"Author","values":["Hallinan, Liam"]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["0000000202707486"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2025-08-27"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/394049"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["control","power systems","optimal control","distributed optimisation","network systems","small-signal stability","inverse optimal control","nyquist techniques"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://www.repository.cam.ac.uk/bitstreams/0bcc2719-049e-4037-af33-7fbda75b6707/download","http://purl.org/NET/rdflicense/allrightsreserved"]},{"key":"dc:rights.embargodate","label":"Dc Rights Embargodate","values":["2026-12-17"]},{"key":"dc:rights.embargotype","label":"Dc Rights Embargotype","values":["embargo"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.17863/CAM.124143"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://www.repository.cam.ac.uk/bitstreams/d599ae10-b236-43bf-9617-59a10f79ffc0/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Networked systems underpin numerous modern engineering applications, with the concept of decentralised control playing an essential role in regulating the behaviour of large-scale, heterogeneous architectures. 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To address this issue, we use inverse optimal control to derive local sufficient conditions under which decentralised controllers in a general nonlinear networked system minimise a global, performance-related cost functional, while simultaneously rendering each subsystem passive. We show that this result can be used for control synthesis in linear systems, which is demonstrated with a DC microgrid example. Furthermore, we extend these results to a broad class of nonlinear, nonsmooth primal–dual algorithms used to solve distributed optimisation problems, showing that a set of performance-enhancing augmentations emerges as the optimal solutions to a network-wide cost functional that penalises deviations from optimality during algorithm transients. Part II turns to network stability. Guaranteeing plug-and-play operation through passivity-based methods is often limited in many applications, most notably in AC power systems. 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