'Periodica Polytechnica Budapest University of Technology and Economics'
Abstract
Higher Order Singular Value Decomposition (HOSVD) based complexity reduction
method is proposed in this paper to polytopic model approximation
techniques. The main motivation is that the polytopic model has
exponentially growing computational complexity with the improvement of its
approximation property through, as usually practiced, increasing the density
of local linear models. The reduction technique proposed here is capable of
defining the contribution of each local linear model, which serves to remove
the weakly contributing ones according to a given threshold. Reducing the
number of local models leads directly to the complexity reduction. The
proposed reduction can also be performed on TS fuzzy model approximation
method. A detailed illustrative example of a non-linear dynamic model is
also discussed. The main contribution of this paper is the multi-dimensional
extension of the SVD reduction technique introduced in the preliminary work
[1]. The advantage of this extension is that the HOSVD based technique of
this paper can be applied to polytopic models varying in a multi-dimensional
parameter space unlike the reduction method of [1] which is designed for
one dimensional parameter space