ABSTRACT
Based on the nonlinear dynamic model of immune system, a robust reference therapeutic control of immune response to pathogenic attack is proposed for therapeutic enhancement to match a prescribed immune response under uncertain initial states and environmental disturbances, including continuous intrusion of exogenous pathogens. The worst-case effect of all possible environmental disturbances and uncertain initial states on the reference model matching for a desired reference immune response is minimized for the enhanced immune system, i.e. a robust therapeutic control is designed to match a prescribed immune model reference response from the minimax https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline16_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game perspective. This minimax https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline16_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> reference therapeutic control problem could herein be transformed to a nonlinear equivalent dynamic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline16_3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game problem. The exogenous pathogens and environmental disturbances are considered as a player to maximize (worsen) the reference matching error when the therapeutic control agents are considered as another player to minimize the reference matching error. Since the innate immune system is highly nonlinear, it is not easy to solve the robust model reference therapeutic control problem by the nonlinear dynamic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline16_4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game strategy directly. A fuzzy model is proposed to interpolate several local 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 minimax https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline16_5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> reference therapeutic control problem of nonlinear immune dynamic systems could be easily solved by the proposed fuzzy dynamic https://www.w3.org/1998/Math/MathML"> H ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432941/63df2486-ef31-4a70-9449-3488247ff9a8/content/inline16_6.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> game strategy 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 robust reference therapeutic control method.
