Cheng Peng, Wang Hai, Stojanovic Vladimir, He Shuping, Shi Kaibo, Luan Xiaoli, Liu Fei, Sun Changyin
IEEE Trans Cybern. 2022 Dec;52(12):13623-13634. doi: 10.1109/TCYB.2021.3112699. Epub 2022 Nov 18.
In this article, the problem of the asynchronous fault detection (FD) observer design is discussed for 2-D Markov jump systems (MJSs) expressed by a Roesser model. In general, the FD observer cannot work synchronously with the system, that is, the mode of the observer varies with the mode of the system in line with some conditional transitional probabilities. For dealing with this difficult point, a hidden Markov model (HMM) is employed. Then, combining the H attenuation index and H increscent index, a multiobjective solution to the FD problem is formed. In terms of linear matrix inequality technology, sufficient conditions are gained to guarantee the existence of the asynchronous FD. Simultaneously, an asynchronous FD algorithm is generated to acquire the optimal performance indices. Finally, a numerical example concerned with the Darboux equation is demonstrated to exhibit the soundness of the developed approach.
本文讨论了由Roesser模型表示的二维马尔可夫跳跃系统（MJSs）的异步故障检测（FD）观测器设计问题。一般来说，FD观测器不能与系统同步工作，即观测器的模式根据一些条件转移概率随系统的模式而变化。为了解决这一难点，采用了隐马尔可夫模型（HMM）。然后，结合H衰减指标和H增长指标，形成了FD问题的多目标解决方案。利用线性矩阵不等式技术，得到了保证异步FD存在的充分条件。同时，生成了一种异步FD算法以获得最优性能指标。最后，给出了一个与达布方程相关的数值例子，以证明所提出方法的有效性。
