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

Kuti, József; Galambos, Péter; Bárányi, Péter

doi:10.1109/ines.2014.6909366

Cited by 20 publications

(34 citation statements)

References 18 publications

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“…Because of the qLPV models (as state space representation) can be represented by qLPV functions, the TP transformation can be easily executed [16]. The occurring TP model is a multidimensional tensor product structure consists of convex combination of a high-order core tensor and different weighting functions in appropriate dimensions belong to the parameter vector [15]. The resulting TP models -thankfully the convex hull manipulation -realizes convex polytopic structures, which allows to combine the transformation with LMI-based techniques [16].…”

Section: Tensor Product Model Transformationmentioning

confidence: 99%

“…N formalizes a limited hypercube in the N -dimensional hyperspace -which is determined by the extremes of the scheduling variables [15], [16].…”

Section: Tensor Product Model Transformationmentioning

confidence: 99%

“…In other way, the S(p(t)) can be described as a linear combination of convex weighting functions and the LTI vertex system for each p(t) ∈ Ω, which results convex combination [16], [21]. Accordingly, -through applying a sampling on the parameter space -the TP based polytopic finite element model can be described as follows [16], [22]:…”

Section: Tensor Product Model Transformationmentioning

confidence: 99%

“…The main goal of TP model transformation is to develop TPmodel objects, which are ready for TP-based controller design. The resulting TP model and controller structures includes the uncertainties as a hidden way -moreover, LMI based techniques can be combined with them [15], [16].…”

Section: Introductionmentioning

confidence: 99%

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Tensor product based modeling of tumor growth

Eigner

Rudas

Szakál

et al. 2017

2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC)

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Abstract-The application of the Soft Computing based methods, especially, the Tensor Product (TP) transformation has several beneficial properties from the biological modeling and control point of view, because complex, nonlinear processes can be handled by them effectively. Another advantage of these tools consist on the Linear Parameter Varying (LPV) and Linear Matrix Inequality (LMI) based techniques can be easily connected to them. The aim of this study is to develop TP models, which can describe the tumor growth beside anti-angiogenic treatment. The role of the anti-angiogenic therapies is to decrease the size of the tumor to operable or maintainable level. From control engineering point of view, the treatment process can be formulated as a control task. In this work, we realized two TP models, which approximates the initial transformed model with high accuracy, regardless the kind of input load and without stability problems. The TP models will be used for TP-based controller design on LMI basis.

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Section: Tensor Product Model Transformationmentioning

confidence: 99%

“…N formalizes a limited hypercube in the N -dimensional hyperspace -which is determined by the extremes of the scheduling variables [15], [16].…”

Section: Tensor Product Model Transformationmentioning

confidence: 99%

Section: Tensor Product Model Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tensor product based modeling of tumor growth

Eigner

Rudas

Szakál

et al. 2017

2017 IEEE International Conference on Systems, Man, and Cybernetics (SMC)

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“…The global stability is only particularly true, i.e. if the system trajectory does not exit from the convex hull (the value of p(t) cannot be higher or lower than the predefined values) [11,12].…”

Section: Affine Lpv Configurationmentioning

confidence: 99%

Novel LPV-based Control Approach for Nonlinear Physiological Systems

2017

APH

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The current paper introduces a novel controller design approach dealing with the control of affine Linear Parameter Varying (LPV) systems using the abstract mathematical properties of the LPV parameter space and classical state-feedback design. By the designed controller structure the parameter dependent LPV system mimics a given selected reference LTI system reaching given performance specifications originally prescribed for the reference LTI system. Further, the actual feedback gains are calculated by comparison to the reference control gains -thus, realizing a "relative control". The method is demonstrated on given nonlinear biomedical problems with simulation results under MATLAB.

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

Kuti

Galambos

Bárányi

2016

Asian Journal of Control

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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.

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

Cited by 20 publications

References 18 publications

Tensor product based modeling of tumor growth

Tensor product based modeling of tumor growth

Novel LPV-based Control Approach for Nonlinear Physiological Systems

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

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