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Set-Theoretic Gray-Box Process Modelling


R. Pearson, M. Pottmann

Politecnico di Torino, Torino, Italy, Dipartimento di Automatica e Informatica

Many techniques have been proposed for model-based computer control of complex physical systems like manufacturing processes, but it has been noted repeatedly that one of the main obstacles to wider application of these approaches is the lack of suitable process models. In particular, fundamental models tend to be much too complex for direct use, while purely empirical modelling has been characterized as an ill-posed problem because it is possible to achieve essentially the same goodness-of-fit with models whose general qualitative behavior differs radically (e.g., stable vs. unstable, minimum-phase vs. nonminimum-phase, etc.). "Gray-box modelling" generally refers to strategies that attempt to combine both fundamental knowledge and empirical data to obtain models of moderate complexity whose qualitative behavior is in reasonable agreement with that of the physical process. This talk builds on our previous joint work on the following gray-box modelling strategy: depending on the general nature of a known steady-state characteristic (in particular, unique vs. multiple steady-states) and possibly other criteria, one of three model structures is chosen (Hammerstein, Wiener, or Lur'e), each involving a linear dynamic model and a single static nonlinearity. This nonlinearity may be chosen to exactly match the steady-state characteristic of the process, and the parameters of the linear model may be chosen to best fit available input-output data, subject to a steady-state gain constraint. This talk proposes a set-theoretic extension of this problem formulation to permit approximate matching of a known nominal steady-state locus, subject to bounded approximation errors arising from inaccuracies in the nominal model (e.g., nonideal mixing in CSTR models).


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(05)Plenary/Invited/Honorary Lecture

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