Local extrema refinement-based tensor product model transformation controller with problem independent sampling methods

Several convex hull manipulation methods have been proposed for tensor product (TP) model transformation, such as CNO, INO, IRNO, minimum volume simplex, and optimized CNO. Among the five convex hull manipulation methods, CNO, INO, and IRNO are the most often used convex hull manipulation methods; minimum volume simplex is an analysis method to shrink the tightness value of the TP model transformation, and optimized CNO convex hull manipulation method is used for convex hull rectification; it also uses core tensor unfolding and folding to obtain tight convex hull. However, all these convex hull manipulation methods are designed based on classical sampling method, while the local extrema are often omitted by the classical sampling method. To obtain a more precise sampling model, in this paper, most of the existing convex hull manipulation methods are extended with local extrema refinement strategy; a uniform local extrema refinement-based convex hull manipulation framework is proposed for the existing convex hull manipulation methods. A single gantry system is used for simulation demonstration; results show that local extrema refinement strategy is needed in convex hull manipulation of TP model transformation; it might be a preferable way to enhance classical sampling method. Minimum volume simplex is more suitable than the optimized CNO in convex hull manipulation of TP model transformation with respect to computational efficiency.