The Tensor Product model transformation is a numerical method that is capable of uniformly transforming LPV (linear parameter-varying) dynamic models into polytopic forms, both in a theoretical and algorithmic context. Using the TP model transformation, different optimization and convexity constraints can be considered, and transformations can be executed without any analytical interactions, within a reasonable amount of time (irrespective of whether the model is given in the form of analytical equations resulting from physical considerations, as an outcome of soft computing based identification techniques such as neural networks or fuzzy logic based methods, or as a result of a black-box identification). Thus, the transformation replaces the usual analytical and oftentimes complex conversions with a numerically tractable and straightforward series of operations.
The TP model transformation generates two kinds of polytopic models. Firstly, it numerically reconstructs the HOSVD (Higher Order Singular Value) based canonical form of LPV models. This is a new and unique polytopic representation. This form extracts the unique structure and various important properties of a given LPV model in the same sense as the HOSVD does for matrices and tensors. Secondly, the TP model transformation generates various convex polytopic forms, upon which LMI (Linear Matrix Inequality) based multi-objective control design techniques can immediately be executed in order to satisfy the given control performance requirements.
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