On the interpretation of local models in blended multiple model structures

Robert Shorten, Roderick Murray-Smith, Roger Bjørgan, Henrik Gollee

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The construction of non-linear dynamics by means of interpolating the behaviour of locally valid models offers and attractive and intuitively pleasing method of modelling non-linear systems. The approach is used in fuzzy logic modelling, operating regime based models, and nonlinear statistical models. The model structure suggests that the composite local models can be used to interpret, in some appropriate manner, the overall non-linear dynamics. In this note we demonstrate that the interpretation of these local models, in the context of multiple model structures, is not as straightforward as it might initially appear. We argue that the blended multiple model system can be interpreted in two ways - as an interpolation of linearisations, or as a full parameterisation of the system. The choice of interpretation affects experiment design, parameter identification, and model validation. We then show that, in some cases, the local models give insight into full model behaviour only in a very small region of state space. More alarmingly, we demonstrate that for off-equilibrium behaviour, subject to some approximation error, a non-unique parameterisation of the model dynamics exists. Hence, qualitative conclusions drawn from the behaviour of an identified local model, i.e. regarding stable, unstable, nodal or complex behaviour, must be treated with extreme caution. The example of muscle modelling is used to illustrate these points clearly.

IMM technical report 21/97

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Last modified Dec 5, 1997

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