Tensor product based modeling of tumor growth

Abstract

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.

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

“…Many powerful approaches are published on the field of sliding mode control in [29,42,43]. In physiological control the usability of TP model transformation has been demonstrated as well [44][45][46][47][48][49]. Various further theories and applications are studied in .…”