In order to design a control system, we need to model the behaviour of the system being controlled. The models have to capture dynamic behaviour (because most systems have some "memory" or "inertia"), so they usually have the form of differential or difference equations. "Black-box" modelling from data, without trying to model internal physical mechanisms, is also called "system identification" (or "time series analysis"). We often build linear models of systems. Even linear models give rise to complex structural questions, such as: Some of these questions are resolved by using

A related question is how to approximate a given system model by a simpler one. One way of formulating this problem leads to the optimal approximation satisfying a set of polynomial equations, which are known to have a finite set of solutions. We have investigated using constructive algebra (Grobner basis) methods to find the complete set of these solutions exactly, and hence to find the optimal approximate model.

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*This page last updated on 14 September 2005.*