Distributed Control of Interconnected Systems in the Behavioural Framework by Yitao Yan B.E. (Hons) in Chemical Engineering A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy School of Chemical Engineering The University of New South Wales Sydney, Australia December, 2019 Thesis/Dissertation Sheet Surname/Family Name : Yan Given Name/s : Yitao Abbreviation for degree as give in the University calendar : PhD Faculty : Faculty of Engineering School : School of Chemical Engineering Thesis Title : Distributed Control of Interconnected Systems in the Behavioural Framework Abstract 350 words maximum: (PLEASE TYPE) The rapid development of technology has made the design, monitoring and data storage of large-scale, complex interconnected systems possible. These efficient and economical interconnected systems come with a price: the complex dynamics due to convoluted interconnections makes the effective control of such a system incredibly difficult. The behaviour of the subsystems in a network is vastly different than that when it is not, and the inherent uncertainties due to modelling errors may be amplified as a result of the strong interactions. Furthermore, the ability to collect and process large amount of data leads to the paradigm shift from model-centric description to data-centric description or hybrid model/data description of a system. These challenges necessitate the need for a unified foundation for the control of complex systems that is able to admit descriptions of systems other than the conventional differential/difference models. Motivated by these challenges, this thesis aims to develop such a framework for the distributed control of an interconnected system using the behavioural systems theory. As a theory that focuses on analysing the dynamics of the external variables and places the trajectories admissible within the system as the central description of a dynamical system, it is perfect for the construction of a platform that unifies various classes of systems and is effective in the analysis of interconnections. The framework is eventually set up as a completely representation-free structure, allowing for free choice of representations for the systems according to the specific needs. Algorithms for several representation structures are also provided. Declaration relating to disposition of project thesis/dissertation I hereby grant to the University of New South Wales or its agents a non-exclusive licence to archive and to make available (including to members of the public) my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known. 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Candidate’s Name Signature Date (dd/mm/yy) Abstract The rapid development of technology has made the design, monitoring and data storage of large-scale, complex interconnected systems possible. These efficient and economical interconnected systems come with a price: the complex dynamics due to convoluted interconnections make the effective control of such a system incredibly difficult. The behaviour of the subsystems in a network is vastly different than that when it is not, and the inherent uncertainties due to modelling errors may be amplified as a result of the strong interactions. Furthermore, the ability to collect and process large amount of data leads to the paradigm shift from model- centric description to data-centric description or hybrid model/data description of a system. These challenges necessitate the need for a unified foundation for the control of complex systems that is able to admit descriptions of systems not only limited to the conventional differential/difference models. Motivated by these challenges, this thesis aims to develop such a framework for the distributed control of an interconnected system using the behavioural systems theory. As a theory that focuses on analysing the dynamics of the external vari- ables and places the trajectories admissible within the system as the central role of describing a dynamical system, it is perfect for the construction of a platform that unifies various classes of systems and is effective in the analysis of interconnections. The framework is eventually set up as a completely representation-free structure, allowing for free choice of representations for the systems according to the specific v Abstract vi needs. Algorithms for several representation structures are also provided. For the case where the subsystems are represented as linear time-invariant differential systems while the global requirements are specified as 1 type con- H ditions, the control design follows a two-step algorithm. Firstly, the behaviours of the subsystems, the (to-be-designed) controllers as well as the global require- ments are all represented as dissipative dynamical systems with quadratic supply rates, from which the (to-be-determined) controller supply rates can be found. Secondly, parametrisations of the supply rates