Minimal Volume Simplex (MVS) Polytopic Model Generation and Manipulation Methodology for TP Model Transformation

• Published in: Asian journal of control 2017-01, Vol.19 (1), p.289-301
• Main Authors: Kuti, József, Galambos, Péter, Baranyi, Péter
• Format: Article
• Language: English
• Subjects: Closed loop systems; Control systems; Methods; Quadratic programming; Systems and control, TP model transformation, polytopic LPV/qLPV modelling, linear matrix inequality
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.1375

The vertices of a polytopic LPV/qLPV model determine the feasibility of any linear matrix inequality (LMI) based control design as well as the achievable control performance, since the polytope typically includes not only the actual system dynamics. This paper proposes a powerful method to determine suitable polytopic qLPV Tensor‐Product model forms that allows for fine tuning through constraints on the locations of the vertices. The paper shows that these tuning methods are capable of effectively influencing the closed‐loop control performance results from LMI‐based multi‐objective optimisation. The advantages of the proposed methods are their tractability, low computational complexity, as well as their determinism. The key idea behind the proposed methods is to determine vertices in each decoupled parameter‐dimensions of the TP model in such a way that they form a minimal volume enclosing simplex fulfilling further fine tuning conditions on its shape. This is achieved based on the extension of the Minimal Volume Simplex Analysis (MVSA) method, where the volume of the enclosing simplex polytope is minimized by applying Sequential Quadratic Programming with majorization minimization strategy extended with a set of additional constraints influencing the location of certain vertices according to physically established considerations. Besides the comprehensive presentation of the proposed design methodology an expressive numerical example is provided to demonstrate its effectiveness and usability.