The structure of nD systems is considerably more complex than that of their 1D counterparts. This has caused serious problems in establishing a theory of nD systems. In ISIS, substantial progress has been made using a completely different paradigm, the behavioural approach. Under this very natural approach, a system is viewed primarily in terms of its trajectories, rather than in terms of a specific set of defining equations. Behavioural theory also allows the application of a rich body of knowledge from the field of commutative algebra.
Further work addressing a wide range of open problems is planned.
Much of this research has been done in collaboration with colleagues in Germany and Portugal. One important class of 2D systems are the linear repetitive processes. Repetitive processes are characterised by a series of sweeps, termed passes, through a set of dynamics defined over a fixed finite duration known as the pass length. Examples include metal rolling, iterative learning control schemes, and the solution algorithms of nonlinear dynamic optimal control problems based on the maximum principle. Recent work has focused on reachability and controllability properties and the structure and design of feedback control laws.