Tensor product model transformation: Difference between revisions

Revision as of 03:15, 6 June 2016

Revision as of 06:15, 17 June 2017

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:* introduces and defines the rank of the TP function by the dimensions of the parameter vector;

* The above point can be extended to TP models (qLPV models to determine the [[HOSVD]] based canonical fromform of qLPV model to order the main component of the qLPV model). Since the core tensor is <math > N+O </math> dimensional, but the weighting functions are determined only for dimensions <math > n=1 \ldots N </math>, namely the core tensor is constructed from <math > O </math> dimensional elements, therefore the resulting TP form is not unique.

*The core step of the TP model transformation was extended to generate different types of convex TP functions or TP models (TP type polytopic qLPV models), in order to focus on the systematic (numerical and automatic) modification of the convex hull instead of developing new LMI equations for feasible controller design (this is the widely adopted approach). It is worth noting that both the TP model transformation and the LMI-based control design methods are numerically executable one after the other, and this makes the resolution of a wide class of problems possible in a straightforward and tractable, numerical way.

* The TP model transformation is capable of performing trade-off between complexity and accuracy of TP functions <ref name=ykc01 /> via discarding the higher-order singular values, in the same manner as the tensor HOSVD is used for complexity reduction.