CCOR Seminar – Péter Baranyi’s talk

Date: 21 March 2024 (Thursday) 13:00-14:00  

Venue: Corvinus University, Building C, Room C.427 

The Corvinus Centre for Operation Research (CCOR), the Corvinus Institute for Advanced Studies (CIAS), and the Institute of Operations and Decision Sciences invite you to the seminar talk by Professor Péter Baranyi (Corvinus University of Budapest and University of Pannonia). 

We would like to inform you that the lecture will be broadcast online. Please be aware that this broadcast will not utilize professional-grade equipment, and we appreciate your understanding that we cannot ensure the broadcast’s quality.  

If you would like to join online, please send an e-mail to anita dot varga at uni-corvinus dot hu by March 21, 8:00. 

“Tensor product model transformation for linear matrix inequality based design and analysis” 

Abstract 

The development of the TP (Tensor Product) model transformation, commenced approximately two decades ago. The primary objective of the initial variant of TP model transformation was to numerically reconstruct a polytopic tensor product model representation of a given function (given as closed formula, Neural Network, Fuzzy model, black box) or quasi Linear Parameter Varying state-space dynamic model. 

This approach offered several significant advantages, including the determination of the minimum number of required weighting functions of the tensor product by dimensions, thereby minimizing the number of components. Additionally, it provided the opportunity for further reduction by defining a trade-off between approximation accuracy and the number of components through the ranking of their importance based on the L2 norm. 

Subsequently, the TP model transformation was expanded to transform a set of functions into a set of TP models with a shared or partially shared weighting functions. Furthermore, the Pseudo TP model transformation was introduced to derive the TP model representation with a given or partially given weighting function system, and if an exact representation is not feasible, to identify the best approximation based on the L2 norm. 

The subsequent advancements of the TP model transformation primarily focused on ensuring advantageous characteristics of the resulting weighting functions. This emphasis stemmed from the understanding that the characteristics of the weighting functions can determine the nature of the convex hull defined by the vertices of the TP model. 

It was soon discovered that the TP model transformation could generate various alternatives of TP models with distinct characteristics. Consequently, design methods that rely on the vertices can be significantly influenced by the TP model transformation. One notable example is the Linear Matrix Inequality based control design frameworks. Within this framework, the vertices of the controller are derived from the vertices of the TP models, typically through the feasibility of Linear Matrix Inequalities. A comprehensive analysis of the impact of tight or loose convex hulls – derived by TP model transformation – in Linear Matrix Inequality based design has been documented in a number of publications.