Peter Baranyi

Non-simplex enclosing polytope generation concept for Tensor Product model transformation based controller design

In polytopic model-based controller synthesis, the vertices of the model determine the achievable performance characteristics. This paper introduces a new concept, that allows for the sophisticated construction of non-simplex enclosing polytopes. The non-simplex structures in general, have much better descriptor properties than the simplex one that leads to less conservative synthesis. The paper demonstrates the workflow of controller design for a nonlinear system through the example of the TORA (Translational Oscillator with a Rotational Actuator) system. The numerical results clearly show that the proposed approach is capable of excluding non-stabilizable regions located between the exact convex hull and the enclosing simplex. The non-simplex polytope leads to an increased number of vertices but it practically does not influence the viability of Tensor-Product (TP) formalization and the feasibility of controller design while the achievable control performance can be improved significantly.

A Hands-On Demonstration of Control Performance Optimization Using Tensor Product Model Transformation and Convex Hull Manipulation

In polytopic model based controller synthesis, the vertices of the model determine the achievable performance. This paper demonstrates a complete and tractable design process exposing the polytopic qLPV model generation and a polytopeshaping technique through the example of the TORA (Translational Oscillator with a Rotational Actuator) system. The demonstrated apparatus allows for systematically improving the control performance through the manipulation of the polytopic structure based on the MVSA (Minimal Volume Simplex Analysis) algorithm. The proposed approach fits to the framework of TP Model Transformation.

Extension of the Multi-TP Model Transformation to Functions with Different Numbers of Variables

The tensor product (TP) model transformation defines and numerically reconstructs the Higher-Order Singular Value Decomposition (HOSVD) of functions. It plays the same role with respect to functions as HOSVD does for tensors (and SVD for matrices). The need for certain advantageous features, such as rank/complexity reduction, trade-offs between complexity and accuracy, and a manipulation power representative of the TP form, has motivated novel concepts in TS fuzzy model based modelling and control. The latest extensions of the TP model transformation, called the multi- and generalised TP model transformations, are applicable to a set functions where the dimensionality of the outputs of the functions may differ, but there is a strict limitation on the dimensionality of their inputs, which must be the same. The paper proposes an extended version that is applicable to a set of functions where both the input and output dimensionalities of the functions may differ. This makes it possible to transform complete multicomponent systems to TS fuzzy models along with the above-mentioned advantages.