This paper presents a systematic approach to deal with the saturated control of a class of distributed parameter systems that can be modeled by the first-order hyperbolic partial differential equations (PDE). The approach extends (also improves over) the existing fuzzy Takagi–Sugeno (TS) state feedback designs for such systems by applying the concepts of the polynomial sum-of-squares (SOS) techniques. First, a fuzzy-polynomial model via Taylor series is used to model the semilinear hyperbolic PDE system. Second, the closed-loop exponential stability of the fuzzy-PDE system is studied through the Lyapunov theory. This allows us to derive a design methodology in which a more complex fuzzy state-feedback control is designed in terms of a set of SOS constraints, able to be numerically computed via semidefinite programming. Finally, the proposed approach is tested in simulation with the standard example of a nonisothermal plug-flow reactor.

中文翻译：

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一类半线性 PDE 系统的分布式饱和控制：一种 SOS 方法

本文提出了一种系统方法来处理一类可以通过一阶双曲偏微分方程 (PDE) 建模的分布式参数系统的饱和控制。该方法通过应用多项式平方和 (SOS) 技术的概念，扩展（也改进了）此类系统的现有模糊 Takagi-Sugeno (TS) 状态反馈设计。首先，通过泰勒级数的模糊多项式模型用于对半线性双曲偏微分方程系统建模。其次，通过李雅普诺夫理论研究了模糊偏微分方程系统的闭环指数稳定性。这使我们能够推导出一种设计方法，其中根据一组 SOS 约束设计更复杂的模糊状态反馈控制，能够通过半定编程进行数值计算。最后，