Abstract
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.