Tsai Shun-Hung, Wang Jun-Wei, Song En-Shou, Lam Hak-Keung
IEEE Trans Cybern. 2021 Jul;51(7):3789-3801. doi: 10.1109/TCYB.2019.2942685. Epub 2021 Jun 23.
This article addresses the H stabilization problems for a class of nonlinear distributed parameter systems which is described by the first-order hyperbolic partial differential equations (PDEs). First, the first-order hyperbolic PDE systems are identified as a polynomial fuzzy PDE system and the polynomial fuzzy controller for the polynomial fuzzy PDE system is proposed. By utilizing the proposed homogeneous polynomial Lyapunov functional, Euler's homogeneous function theorem, and the proposed theorems, a spatial derivative sum-of-squares (SDSOS) exponential stabilization condition is proposed. In addition, a recursive algorithm for the SDSOS exponential stabilization condition is developed to find the feasible solution. Furthermore, in order to reduce the conservatism of the proposed results, a relaxed H stabilization condition for the polynomial fuzzy PDE system is provided. Finally, the nonisothermal plug-flow reactor (PFR) is used to demonstrate the effectiveness and feasibility of the proposed method.
本文研究了一类由一阶双曲型偏微分方程（PDEs）描述的非线性分布参数系统的H稳定性问题。首先，将一阶双曲型PDE系统识别为多项式模糊PDE系统，并提出了该多项式模糊PDE系统的多项式模糊控制器。通过利用所提出的齐次多项式李雅普诺夫泛函、欧拉齐次函数定理以及所提出的定理，提出了一种空间导数平方和（SDSOS）指数稳定条件。此外，还开发了一种用于SDSOS指数稳定条件的递归算法以找到可行解。此外，为了降低所提结果的保守性，给出了多项式模糊PDE系统的松弛H稳定条件。最后，通过非等温活塞流反应器（PFR）来证明所提方法的有效性和可行性。
