Sampled-Data Fuzzy Control for Nonlinear Coupled Parabolic PDE-ODE Systems
针对一类由抛物型偏微分方程和常微分方程描述的非线性耦合系统，提出基于T-S模糊模型的采样数据模糊控制器设计方法，保证闭环系统指数稳定，并通过高超声速火箭车仿真验证有效性。
In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.