This paper deals with a fuzzy stabilization design problem for a class of semilinear parabolic partial differential equation (PDE) systems using mobile actuators and sensors. Initially, a Takagi-Sugeno (T-S) fuzzy PDE model is employed to accurately represent the semilinear parabolic PDE system. Subsequently, based on the T-S fuzzy model, a stabilization scheme containing the fuzzy controllers and the guidance of mobile actuator/sensor pairs is proposed, where the spatial domain is decomposed into multiple subdomains according to the number of actuator/sensor pairs and each actuator/sensor pair is capable of moving within the respective subdomain. Then, by a Lyapunov direct technique, an integrated design of fuzzy controllers plus mobile actuator/sensor guidance laws is developed in the form of bilinear matrix inequalities (BMIs), such that the resulting closed-loop system is exponentially stable and the mobile actuator/sensor guidance can enhance the transient performance of the closed-loop system. Furthermore, an iterative algorithm based on linear matrix inequalities is proposed to solve the BMIs. Finally, two examples are given to illustrate the effectiveness of the proposed method.

中文翻译：

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具有移动执行器和传感器的半线性抛物线偏微分方程系统的模糊稳定设计


本文研究了一类使用移动执行器和传感器的半线性抛物型偏微分方程 (PDE) 系统的模糊稳定性设计问题。最初，采用 Takagi-Sugeno (TS) 模糊 PDE 模型来准确表示半线性抛物线 PDE 系统。随后，基于TS模糊模型，提出了一种包含模糊控制器和移动执行器/传感器对引导的稳定方案，其中根据执行器/传感器对的数量和每个执行器/传感器将空间域分解为多个子域。传感器对能够在各自的子域内移动。然后，通过李亚普诺夫直接技术，以双线性矩阵不等式（BMI）的形式开发了模糊控制器和移动执行器/传感器制导律的集成设计，使得所得闭环系统呈指数稳定，并且移动执行器/传感器引导可以增强闭环系统的瞬态性能。此外，提出了一种基于线性矩阵不等式的迭代算法来求解BMI。最后，给出两个例子来说明所提方法的有效性。