Zhang Xiao-Wei, Wu Huai-Ning
IEEE Trans Cybern. 2022 May;52(5):3947-3956. doi: 10.1109/TCYB.2020.3020087. Epub 2022 May 19.
Via mobile sensing measurements, this study applies the Takagi-Sugeno (T-S) fuzzy model to deal with the mobile fuzzy control design problem for nonlinear time-delay parabolic partial differential equation (PDE) systems. Initially, we use a T-S fuzzy model to accurately represent the nonlinear time-delay parabolic PDE system. Subsequently, under the assumption that the actuators and sensors are collocated while the spatial domain is divided by several subdomains, a control scheme containing the fuzzy controllers and the guidance of mobile actuator/sensor pairs is proposed based on the obtained T-S fuzzy model, where the projection modification guidance to be designed can guarantee that each mobile actuator/sensor pair moves within the prescribed area. Then, using the Lyapunov direct method and integral inequalities, a membership-function-dependent design of fuzzy controllers plus mobile actuator/sensor guidance laws is developed to render the resulting closed-loop time-delay system exponentially stable. Moreover, the exponential decay rate can also be increased by the proposed mobile guidance laws. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed design method and the application of mobile actuator/sensor pairs contributes to accelerating the convergence speed of the closed-loop state.
通过移动感知测量，本研究应用高木-关野（T-S）模糊模型来处理非线性时滞抛物型偏微分方程（PDE）系统的移动模糊控制设计问题。首先，我们使用T-S模糊模型来精确表示非线性时滞抛物型PDE系统。随后，在假设执行器和传感器是共置的且空间域被划分为若干子域的情况下，基于所获得的T-S模糊模型，提出了一种包含模糊控制器和移动执行器/传感器对引导的控制方案，其中要设计的投影修正引导能够保证每个移动执行器/传感器对在规定区域内移动。然后，利用李雅普诺夫直接法和积分不等式，开发了一种依赖于隶属函数的模糊控制器设计以及移动执行器/传感器引导律，以使所得的闭环时滞系统指数稳定。此外，所提出的移动引导律还可以提高指数衰减率。最后，给出了数值模拟结果，以说明所提出设计方法的有效性，并且移动执行器/传感器对的应用有助于加快闭环状态的收敛速度。
