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Robust Control of Immune Systems Under Noises: Stochastic Game Approach

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Handbook of Statistical Bioinformatics

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

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Abstract

A robust control of immune response is proposed for therapeutic en- hancement to match a prescribed immune response under uncertain initial states and environmental noises, including continuous intrusion of exogenous pathogens. The worst-case effect of all possible noises and uncertain initial states on the matching for a desired immune response is minimized for the enhanced immune system, i.e., a robust control is designed to track a prescribed immune model response from the stochastic minimax matching perspective. This minimax matching problem could herein be transformed to an equivalent stochastic game problem. The exogenous pathogens and environmental noises (external noises) and stochastic uncertain internal noises are considered as a player to maximize (worsen) the matching error when the therapeutic control agents are considered as another player to minimize the matching error. Since the innate immune system is highly nonlinear, it is not easy to solve the robust control problem by the nonlinear stochastic game method directly. A fuzzy model is proposed to interpolate several linearized immune systems at different operating points to approximate the innate immune system via smooth fuzzy membership functions. With the help of fuzzy approximation method, the stochastic minimax matching control problem of immune systems could be easily solved by the proposed fuzzy stochastic game method via the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. Finally, in silico examples are given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed method.

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Authors and Affiliations

  1. Department of Electrical Engineering, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan

    Bor-Sen Chen & Chia-Hung Chang

  2. Institute of Bioinformatics and Structural Biology, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan

    Yung-Jen Chuang

Authors
  1. Bor-Sen Chen
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  2. Chia-Hung Chang
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  3. Yung-Jen Chuang
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Corresponding author

Correspondence to Bor-Sen Chen .

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Editors and Affiliations

  1. , Institute of Statistics, National Chiao Tung University, Ta Hsueh Road 1001, Hsinchu, 30050, Taiwan, Taiwan R.O.C.

    Henry Horng-Shing Lu

  2. , Department of Empirical Inference, MPI for Intelligent Systems, Spemannstraße 38, Tübingen, 72076, Germany

    Bernhard Schölkopf

  3. School of Medicine, Dept. Epidemiology & Public Health, Yale University, College Street 60, New Haven, 06520, Connecticut, USA

    Hongyu Zhao

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Chen, BS., Chang, CH., Chuang, YJ. (2011). Robust Control of Immune Systems Under Noises: Stochastic Game Approach. In: Lu, HS., Schölkopf, B., Zhao, H. (eds) Handbook of Statistical Bioinformatics. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16345-6_27

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