The Canonical Controller for Distributed Systems
Abstract
This paper generalises results of Willems-Trentelman, and van der Schaft, on achievable behaviours, to the case of linear distributed systems defined by partial differential or difference equations. It shows that the `minimal' controller which achieves a particular subsystem is the canonical controller of van der Schaft, thereby answering the `open problem' of sc in the setting of infinite dimensional and n-D systems. This result is used to describe the collection of all linear subsystems of the electro-magnetic field, containing the vacuum solutions, that can be achieved by suitable choices of electric charge and current density.
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