In this paper, an observer-based H∞ sampled-data fuzzy control problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems. With the aid of the modal decomposition technique, a nonlinear ordinary differential equation (ODE) model is initially derived to describe the dominant (slow) dynamics of the PDE system. Subsequently, the resulting nonlinear ODE model is accurately represented by the Takagi-Sugeno (T-S) fuzzy model. Then, based on the T- S fuzzy model, a finite-dimensional observer-based sampled-data fuzzy control design with H∞ performance is developed for the PDE system via employing a novel time-dependent functional. The outcome of the observer-based H∞ sampled-data fuzzy control problem can be formulated as a bilinear matrix inequality optimization problem. Moreover, an iterative optimization algorithm based on the linear matrix inequalities is given to obtain a suboptimal H∞ sampled-data fuzzy controller. Finally, simulation results on the Fisher equation and a temperature cooling fin of high-speed aerospace vehicle illustrate that the proposed design method is effective.

中文翻译：

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一类非线性抛物型 PDE 系统的基于观测器的 $H_{\infty }$ 采样数据模糊控制


本文针对一类非线性抛物型偏微分方程 (PDE) 系统解决了基于观测器的 H∞ 采样数据模糊控制问题。借助模态分解技术，首先导出非线性常微分方程 (ODE) 模型来描述 PDE 系统的主导（慢速）动力学。随后，所得的非线性 ODE 模型由 Takagi-Sugeno (TS) 模糊模型准确表示。然后，基于T-S模糊模型，通过采用一种新颖的瞬态泛函，为偏微分方程系统开发了一种具有H∞性能的基于有限维观测器的采样数据模糊控制设计。基于观测器的 H∞ 采样数据模糊控制问题的结果可以表示为双线性矩阵不等式优化问题。此外，还给出了基于线性矩阵不等式的迭代优化算法，以获得次优的H∞采样数据模糊控制器。最后，对Fisher方程和高速航天飞行器温度冷却翅片的仿真结果表明，所提出的设计方法是有效的。