H∞ Observer-based Tracking Control of Stochastic Immune Systems under Environmental Disturbances and Measurement Noises

A robust H∞ observer-based tracking control of stochastic immune response is proposed for therapeutic enhancement to track a prescribed immune response under uncertain initial states, environmental disturbances and measurement noises. The statistics of initial condition, environmental and measurement noises are assumed unavailable. Further, the state variables may not all be available and may be corrupted by measurement noises. Therefore, an observer-based control design is proposed for robust H∞ observer-based tracking control of stochastic immune systems. The robust H∞ control is designed to track a prescribed immune model response in spite of environmental disturbances, uncertain initial conditions and measurement noises. Since the stochastic immune system is highly nonlinear, it is not easy to solve the robust H∞ observer-based tracking control problem directly. A fuzzy model is proposed to interpolate several linearized stochastic immune systems to approximate the nonlinear stochastic immune system via smooth fuzzy membership functions. By the fuzzy approximation method, the H∞ observer-based tracking control problem of stochastic immune systems could be easily solved via the linear matrix inequality (LMI) technique with the help of Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency of the proposed method.