Interaction measure determines decentralized and sparse control configurations for a multivariable process control. This paper investigates interval type-2 Takagi–Sugeno fuzzy (IT2TSF) model based interaction measures using two different criteria, one is controllability and observability gramians, the other is relative normalized gain array (RNGA). The main contributions are: first, a data-driven IT2TSF modeling method is introduced; second, explicit formulas to execute the two measures based on IT2TSF models are given; third, two interaction indexes are defined from RNGA to select sparse control configuration; fourth, the calculations to derive sensitivities of the two measures with respect to parametric variations in the IT2TSF models are developed; and fifth, the discussion to compare the two measures is presented. Three multivariable processes are used as examples to show that the results calculated from IT2TSF models are more accurate than that from their type-1 counterparts, and compared to gramian-based measure, RNGA selects more reasonable control configurations and is more robust to the parametric uncertainties.

中文翻译：

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基于区间2型Takagi-Sugeno模糊模型的控制配置选择交互测度

交互度量确定了多变量过程控制的分散和稀疏控制配置。本文使用两种不同的标准研究基于区间类型 2 Takagi-Sugeno 模糊 (IT2TSF) 模型的交互测量，一个是可控性和可观察性格拉姆，另一个是相对归一化增益阵列 (RNGA)。主要贡献有：首先，介绍了一种数据驱动的IT2TSF建模方法；其次，给出了基于IT2TSF模型执行这两项措施的明确公式；第三，从RNGA中定义了两个交互指标来选择稀疏控制配置；第四，计算得出两种测量对 IT2TSF 模型中参数变化的敏感性；第五，提出了比较这两种措施的讨论。