$H_\infty $ Disturbance Attenuation for Nonlinear Coupled Parabolic PDE–ODE Systems via Fuzzy-Model-Based Control Approach
针对一类由非线性常微分方程和半线性抛物型偏微分方程耦合的系统，设计了H∞模糊控制器，通过分段均匀执行器和点传感器实现指数稳定并满足干扰抑制性能，仿真验证了有效性。
An H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy control design is presented for the disturbance attenuation of a class of coupled systems described by a set of nonlinear ordinary differential equations (ODEs) and a semi-linear parabolic partial differential equation (PDE). The fuzzy control scheme consists of an ODE state feedback fuzzy subcontroller for the ODE subsystem and a PDE static output feedback fuzzy subcontroller for the PDE subsystem by using piecewise uniform actuators and pointwise sensors. Initially, the original nonlinear system is accurately represented by employing a Takagi-Sugeno fuzzy coupled parabolic PDE-ODE model. Then, an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fuzzy controller is developed to exponentially stabilize the fuzzy coupled system while satisfying a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of disturbance attenuation, whose existence condition is given by linear matrix inequalities. Finally, simulation results on a hypersonic rocket car are given to show the effectiveness of the proposed design method.