Jozsef Kuti

55955766900

Publications - 5

Control Analysis and Synthesis through Polytopic Tensor Product Model: a General Concept

Péter Galambos Jozsef Kuti P. Baranyi

Publication Name: IFAC Papersonline

Publication Date: 2017-07-01

Volume: 50

Issue: 1

Page Range: 6558-6563

Description:

The paper revisits and renew the concept of Polytopic Tensor Product (TP) Model based control analysis and synthesis by generalizing the use of TP-structured variables in the definite conditions derived from the applied control criteria. For TP forms that can depend on multivariate parameter sets (optionally with two times or larger multiplicities), a compact TP formalism is proposed where the multiplicity vector describes the structure. By setting the multiplicities, the parameter dependencies can be neglected or considered with arbitrary high complexity in the variables of controller-candidate, Lyapunov-function candidate and slack variables as well. The paper points out that the definite conditions on the structures of these variables results in definite conditions on Polytopic TP forms enabling a recursive method to reformulate them into Linear Matrix Inequalities (LMIs), Bilinear Matrix Inequalities (BMIs), etc. according to the design method in consideration. The application of the novel concept is shown through H∞ state feedback design for Linear Parameter Varying (LPV) systems.

Open Access: Yes

DOI: 10.1016/j.ifacol.2017.08.611

Generalization of Tensor Product Model Transformation for Control Design

Péter Galambos Jozsef Kuti P. Baranyi

Publication Name: IFAC Papersonline

Publication Date: 2017-07-01

Volume: 50

Issue: 1

Page Range: 5604-5609

Description:

The paper shows that the separated structure of parameter dependencies within the Polytopic Tensor-Product (TP) model can be exploited during the controller design by applying controller candidates that depend only on certain parameter sets. This approach combines the polytopic uncertainty and Parallel Distributed Compensation (PDC) concepts in such a way that they become special cases of the proposed formulation. Motivated by this recognition and the fact that the separation of parameter dependencies increases the complexity and computational cost, the definition of Polytopic TP representation for LPV/qLPV models is relaxed. The new definition allows for the use of arbitrarily chosen parameter sets in the model - according to the control goals - and the separation can be performed only for these sets. Through the derivation, an appropriate transformation algorithm and the unique Affine TP model is introduced discussing the related concepts of tensor algebra and affine geometry as well.

Open Access: Yes

DOI: 10.1016/j.ifacol.2017.08.1106

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

Péter Galambos Jozsef Kuti P. Baranyi

Publication Name: 2016 IEEE International Conference on Systems Man and Cybernetics Smc 2016 Conference Proceedings

Publication Date: 2017-02-06

Volume: Unknown

Issue: Unknown

Page Range: 3368-3373

Description:

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.

Open Access: Yes

DOI: 10.1109/SMC.2016.7844754

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

Péter Galambos Jozsef Kuti P. Baranyi

Publication Name: Asian Journal of Control

Publication Date: 2017-01-01

Volume: 19

Issue: 1

Page Range: 289-301

Description:

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.

Open Access: Yes

DOI: 10.1002/asjc.1375

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

Péter Galambos P. Várlaki Jozsef Kuti P. Baranyi

Publication Name: Proceedings 2015 IEEE International Conference on Systems Man and Cybernetics Smc 2015

Publication Date: 2016-01-12

Volume: Unknown

Issue: Unknown

Page Range: 2609-2614

Description:

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.

Open Access: Yes

DOI: 10.1109/SMC.2015.456