This paper concentrates on the study of the decentralized fuzzy control method for a class of fractional-order interconnected systems with unknown control directions. To overcome the difficulties caused by the multiple unknown control directions in fractional-order systems, a novel fractional-order Nussbaum function technique is proposed. This technique is much more general than those of existing works since it not only handles single/multiple unknown control directions but is also suitable for fractional/integer-order single/interconnected systems. Based on this technique, a new decentralized adaptive control method is proposed for fractional-order interconnected systems. Smooth functions are introduced to compensate for unknown interactions among subsystems adaptively. Furthermore, fuzzy logic systems are utilized to approximate unknown nonlinearities. It is proven that the designed controller can guarantee the boundedness of all signals in interconnected systems and the convergence of tracking errors. Two examples are given to show the validity of the proposed method.

中文翻译：

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未知控制方向分数阶互联系统的自适应模糊控制

本文重点研究一类控制方向未知的分数阶互联系统的分散模糊控制方法。为了克服分数阶系统中多个未知控制方向带来的困难，提出了一种新的分数阶Nussbaum函数技术。该技术比现有工作的技术更通用，因为它不仅可以处理单个/多个未知控制方向，而且还适用于分数/整数阶单/互连系统。基于该技术，针对分数阶互联系统提出了一种新的分散自适应控制方法。引入平滑函数以自适应地补偿子系统之间的未知交互。此外，模糊逻辑系统用于逼近未知的非线性。证明所设计的控制器能够保证互连系统中所有信号的有界性和跟踪误差的收敛性。给出了两个例子来证明所提出方法的有效性。