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A TP-LPV-LMI Approach to Control of Tumor Growth

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Book cover Recent Advances in Intelligent Engineering

Part of the book series: Topics in Intelligent Engineering and Informatics ((TIEI,volume 14))

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Abstract

By using advanced control techniques to control physiological systems sophisticated control regimes can be realized. There are several challenges need to be solved in these approaches, however. Most of the time, the lack of information of the internal dynamics, the nonlinear behavior of the system to be controlled and the variabilities coming from that simple fact that people are different and their specifics vary in time makes the control design difficult. Nevertheless, the use of appropriate methodologies can facilitate to find solutions to them. In this study, our aim is to introduce different techniques and by combining them we show an effective way for control design with respect to physiological systems. Our solution stands on four pillars: transformation of the formulated model into control oriented model (COM) form; use the COM for linear parameter varying (LPV) kind modeling to handle unfavorable dynamics as linear dependencies; tensor product modeling (TPM) to downsize the computational costs both from modeling and control design viewpoint; and finally, using linear matrix inequalities (LMI) based controller design to satisfy predefined requirements. The occurring TP-LPV-LMI controller is able to enforce a given, nonlinear system to behave as a selected reference system. In this study, the detailed control solution is applied for tumor growth control to maintain the volume of the tumor.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 679681).

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Author information

Authors and Affiliations

  1. Physiological Controls Research Center, Research, Innovation and Service Center of Óbuda University, Budapest, Hungary

    György Eigner & Levente Kovács

Authors
  1. György Eigner
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  2. Levente Kovács
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Correspondence to Levente Kovács .

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Editors and Affiliations

  1. Obuda University, Budapest, Hungary

    Levente Kovács

  2. Óbuda University, Budapest, Hungary

    Tamás Haidegger

  3. Óbuda University, Budapest, Hungary

    Anikó Szakál

Appendix

Appendix

1.1 Notations and Abbreviations

For the notations and abbreviations applied in this study please see Tables 1 and 2.

Table 1 General Phrases
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Table 2 Mathematical terms
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Eigner, G., Kovács, L. (2020). A TP-LPV-LMI Approach to Control of Tumor Growth. In: Kovács, L., Haidegger, T., Szakál, A. (eds) Recent Advances in Intelligent Engineering. Topics in Intelligent Engineering and Informatics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-14350-3_12

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