Jan Maciejowski's research: System identification and Modelling

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:
  • How to avoid redundant parameters?
  • How to ensure the model is stable when the real system is known to be stable?
  • What is the appropriate model complexity to explain observed behaviour?
  • Some of these questions are resolved by using balanced parametrizations. A class of algorithms known as subspace methods has proved to be very effective in practice. We have explored the use of balanced parametrizations, and proposed improved subspace methods. We have also developed extensions of subspace methods for the identification of bilinear models (in which state-input products are allowed).

    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.

  • Balanced parametrizations and subspace methods: Publications and software
  • ERNSI: European Research Network on System Identification
  • UCAM: University of Cambridge Team
  • ERNSI home page

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    This page last updated on 14 September 2005.