Minimal Volume Simplex (MVS) approach for convex hull generation in TP Model Transformation

摘要

To a large degree, systems and control applications of TP Model Transformation rely on convex hull manipulation of polytopic LPV/qLPV system models. In this respect, the creation of tight convex hulls is an especially challenging problem, as it requires complex nonlinear optimisation. By defining the Minimal Volume Simplex (MVS) type hull, the paper presents a novel approach for tight convex hull generation. The approach, which involves the so-called MVSA algorithm, leads to a radical reduction in computational time while showing improved numerical properties in terms of repeatability and reliability as compared to other hull generation methods. Furthermore, the proposed method allows for the taking into account of special design considerations regarding the alignment of the convex hull.