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This paper formulates a framework for the analysis and distributed control ofinterconnected systems from the behavioural perspective. The discussions arecarried out from the viewpoint of set theory and the results are completelyrepresentation-free. The core of a dynamical system can be represented as theset of all trajectories admissible through the system and interconnections areinterpreted as constraints on the choice of trajectories. We develop astructure in which the interconnected behaviour can be directly built from thebehaviours of the subsystems in an explicit way without any presumed forms ofrepresentations. We show that the interconnected behaviour can also be fullyobtained from local observations of the subsystem. Furthermore, we develop thenecessary and sufficient conditions for the existence of distributed controllerbehaviours and their explicit construction. Due to the entirelyrepresentation-free nature of this framework, it unites various representationsand descriptions of features of dynamical systems (e.g. models, dissipativity,data, etc.) as behaviours, allowing for the formation of a unified platform forthe analysis and distributed control for interconnected systems.

Behavioural Approach to Distributed Control of Interconnected Systems