在未知的初始值、環境干擾和外來病原體入侵下，免疫反應的強健模式匹配控制設計可用在加強藥物的治療上，達到我們所需求的免疫反應。在所有可能未知的初始值、環境干擾和外來病原體入侵的最壞影響之下，我們需要加強免疫反應，伴隨著極小極大化匹配需求的免疫反應是要最小化的。這意思是說設計強健模式匹配控制是來追蹤我們所需求的免疫反應，利用極小極大化匹配的觀點。這個極小極大化匹配的問題可以被轉換成等效的動態博局問題。當外來的病原體和環境的干擾被視為一個玩家，其目的是來增大匹配誤差，治療的藥劑控制考慮成為另一個玩家來減小匹配誤差。由於，先天免疫系統是非線性的，這不是很容易直接用非線性的動態博局方法來解強健模式匹配控制的問題。所以吾人利用模糊模式的方法在不同的操作點之下，透過平滑的糢糊歸屬函數來內插成許多線性的免疫系統，用此方法來近似非線性的先天免疫系統。然後極小極大化匹配控制的問題就可以簡單地轉換成線性的動態博局方法，並且透過Matlab 7.0裡面的LMI toolbox的技術解決出來。最後，有一些計算模擬的例子利用電腦模擬呈現，來驗證此方法的實用及功效。

A robust model matching control of immune response is proposed for therapeutic enhancement to match a prescribed immune response under uncertain initial states and environmental disturbances, including exogenous pathogen input. The worst-case effect of all possible environmental disturbances and uncertain initial states on the min-max matching with a desired immune response is minimized for the enhanced immune system, i.e. the robust min-max model matching control is designed to track a prescribed immune model response from the min-max matching perspective. This min-max matching problem could be transformed to an equivalent dynamic game problem. The exogenous pathogen and environmental disturbances are considered as a player to maximize (worsen) the matching error when the therapeutic control agents are considered as a player to minimize the matching error. Since the innate immune system is highly nonlinear, it is not easy to solve the robust model matching control problem by the nonlinear dynamic game method directly. A fuzzy model is proposed to interpolate several linearized immune systems at different operation points to approximate the innate immune system via smooth fuzzy membership functions. With the help of fuzzy approximation method, the min-max matching control problem of immune systems could be easily solved by linear dynamic game method via the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab [3]. Finally, few computational simulation examples are given in silicon to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed method.

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