Complex Systems - Simple Models?

Abstract In this contribution, the relation between the intended purpose of a model and its required degree of accuracy is investigated. It is based on an intuitive definition of accuracy from J. C. WILLEMS’ “behavioural systems theory᾿. We outline a procedure that generates a strictly ordered set of abstractions, or approximations, for a given detailed model, where ordering is in the sense of approximation accuracy. It is particularly useful for the purpose of control synthesis: within the set of abstractions, there exists a unique coarsest, i.e. least accurate, model that allows a given specification to be met. The resulting control scheme is guaranteed to “work properly᾿ for the underlying detailed model. The approach is illustrated by a number of examples from process control.