Kong Shulan, Lu Mingying, Li Mutian
School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China.
Department of Applied Mathematics, University of Washington, Seattle, 98195, WA, US.
Sci Rep. 2024 Dec 28;14(1):30958. doi: 10.1038/s41598-024-82083-6.
This research investigates detectability of a class of mix-valued logical control networks through the application of a Luenberger-like observer. First, three concepts of detectability: detectability, strong detectability, and weak detectability are defined for the mix-valued logical control networks. Subsequently, the equivalent algebraic form of the control networks is obtained to deal with the three kinds of detectability. A Luenberger-like observer for the equivalent algebraic representation is designed to tackle the challenges. Then some necessary and sufficient conditions for detectability are derived by employing the observer associated with detecting the states of the control networks. Finally, two examples are presented to effectively demonstrate our obtained conclusions in both theory and applications. Moreover it is shown that our proposed observer scheme has good performance.
本研究通过应用类Luenberger观测器来研究一类混合值逻辑控制网络的可检测性。首先，为混合值逻辑控制网络定义了三种可检测性概念：可检测性、强可检测性和弱可检测性。随后，得到了控制网络的等价代数形式以处理这三种可检测性。设计了一个用于等价代数表示的类Luenberger观测器来应对挑战。然后，通过使用与检测控制网络状态相关的观测器，推导出了可检测性的一些充要条件。最后，给出了两个例子，有效地证明了我们在理论和应用方面得出的结论。此外，结果表明我们提出的观测器方案具有良好的性能。
