On the interpretation of local models in blended multiple model
structures
Robert Shorten, Roderick Murray-Smith, Roger Bjørgan, Henrik Gollee
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Abstract
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
IMM publications list
Last modified Dec 5, 1997
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