Descriptor Representation-Based Guaranteed Cost Control Design Methodology for Polynomial Fuzzy Systems
Descriptor Representation-Based Guaranteed Cost Control Design Methodology for Polynomial Fuzzy Systems
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DOI：
10.3390/pr10091799
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发表时间：
2022-09
期刊：
影响因子：
3.5
通讯作者：
Yu-Hsuan Shen;Ying-Jen Chen;Fan-Nong Yu;Wen-June Wang;Kazuo Tanaka
中科院分区：
文献类型：
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作者：
Yu-Hsuan Shen;Ying-Jen Chen;Fan-Nong Yu;Wen-June Wang;Kazuo Tanaka
提出了一种基于广义表示的多项式模糊系统保性能设计方法。该方法利用描述符表示法将多项式模糊模型的闭环系统与基于并行分布补偿(PDC)的模糊控制器相结合。通过使用描述符表示法，保成本控制(GCC)设计分析可以利用多项式模糊松弛矩阵来获得较不保守的结果。提出的GCC设计是以平方和为条件的。多项式模糊松弛矩阵的应用导致了控制设计中的双重模糊求和问题。因此，共正松弛法很好地解决了这一问题，并被用于控制设计分析中。GCC的设计将预先指定的成本函数的上限降至最低。根据性能函数，给出了两个仿真算例，验证了GCC设计的有效性。在这两个实例中，所提出的设计取得了较好的结果。
This paper presents a descriptor representation-based guaranteed cost design methodology for polynomial fuzzy systems. This methodology applies the descriptor representation for presenting the closed-loop system of the polynomial fuzzy model with a parallel distributed compensation (PDC) based fuzzy controller. By the utility of descriptor representation, the guaranteed cost control (GCC) design analysis can utilize polynomial fuzzy slack matrices for obtaining less conservative results. The proposed GCC design is presented as the sum-of-squares (SOS) conditions. The application of polynomial fuzzy slack matrices leads to the double fuzzy summation issue in the control design. Accordingly, the copositive relaxation works out the problem well and is adopted in the control design analysis. The GCC design minimizes the upper limit of a predesignated cost function. According to the performance function, two simulation examples are provided to demonstrate the validity of the proposed GCC design. In these two examples, the proposed design obtains superior results.