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Mixed H-2/H-infinity fuzzy proportional-spatial integral control design for a class of nonlinear distributed parameter systems

机译：一类非线性分布参数系统的混合H-2 / H无穷模糊比例空间积分控制设计

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In this paper, a fuzzy feedback control design problem with a mixed H-2/H-infinity performance is addressed by using the distributed proportional-spatial integral (P-sI) control approach for a class of nonlinear distributed parameter systems represented by semi linear parabolic partial differential-integral equations (PDIEs). The objective of this paper is to develop a fuzzy distributed P-sI controller with a mixed H-2/H-infinity performance index for the semi-linear parabolic PDIE system. To do this, the semi-linear parabolic PDIE system is first assumed to be exactly represented by a Takagi-Sugeno (T-S) fuzzy parabolic PDIE model in a given local domain of Hilbert space. Then, based on the T-S fuzzy PDIE model, a distributed fuzzy P-sI state feedback controller is proposed such that the closed-loop PDIE system is locally exponentially stable with a mixed H-2/H-infinity performance. The sufficient condition on the existence of the fuzzy controller is given by using the Lyapunov's direct method, the technique of integration by parts, and vector-valued Wirtinger's inequalities, and presented in terms of standard linear matrix inequalities (LMIs). Moreover, by using the existing LMI optimization techniques, a suboptimal H-infinity fuzzy controller is derived in the sense of minimizing an upper bound of a given H-2 performance function. Finally, the developed design methodology is successfully applied to feedback control of a semi-linear reaction diffusion system with spatial integral terms. (C) 2016 Elsevier B.V. All rights reserved.
机译：本文针对半线性表示的一类非线性分布参数系统，采用分布式比例空间积分（P-sI）控​​制方法，解决了混合H-2 / H无穷性能的模糊反馈控制设计问题。抛物线偏微分积分方程（PDIE）。本文的目的是为半线性抛物线PDIE系统开发具有H-2 / H无穷混合性能指标的模糊分布式P-sI控制器。为此，首先假定半线性抛物线PDIE系统在给定的希尔伯特空间局部域中由Takagi-Sugeno（T-S）模糊抛物线PDIE模型精确表示。然后，基于T-S模糊PDIE模型，提出了一种分布式模糊P-sI状态反馈控制器，以使闭环PDIE系统具有混合H-2 / H无穷大性能的局部指数稳定。使用李雅普诺夫直接法，零件积分技术和矢量值维特林格不等式给出了模糊控制器存在的充分条件，并以标准线性矩阵不等式（LMI）表示。而且，通过使用现有的LMI优化技术，从使给定H-2性能函数的上限最小化的意义上，得出了次优H-无限模糊控制器。最后，所开发的设计方法已成功地应用于具有空间积分项的半线性反应扩散系统的反馈控制。 （C）2016 Elsevier B.V.保留所有权利。

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