Simultaneous fault estimation for uncertain Markovian jump systems subjected to actuator degradation

Abstract

Summary This paper investigates simultaneous estimations of states, system fault, and sensor fault for a class of Markovian jump systems, resorting to the design of a robust observer, in which both the external disturbance and actuator degradation are taken into consideration. The loss‐of‐effectiveness, stuck, and outage fault cases are involved, and the considered Markovian jump system is assumed to possess generally uncertain transition rates, which can generalize the traditional bounded uncertain transition rates and partially unknown transition rates. In particular, an augmented system whose states cover the original states, system fault, and sensor fault is constructed. Then, a novel adaptive observer is presented with time‐varying gain matrices and parameter accommodation being injected to deal with the disturbance and actuator degradation. Finally, a practical example is shown to demonstrate the high efficiency of the proposed method as well as its advantages over some existing results.

Robust Distributed Fault Diagnosis for Large-Scale Interconnected Multi-Motor Web-Winding Systems

“…Then, sufficient condition of asymptotic stability with the ability to attenuate the norm bounded uncertain disturbances for system (23) or ( 24) will be given in Theorem 2. Meanwhile, the observer gain matrices 2j , K 2j and M 2j can be obtained by solving the LMI.…”

“…In [21], the system faults are firstly modeled as additive and multiplicative unknown dynamics, and then they are estimated by using one-step previous state information. In [22], [23] the adaptive observer is designed to simultaneously estimate the actuator and sensor faults of Markovian jump systems. In [24], a robust state-space observer is proposed to simultaneously estimate the descriptor states, actuator faults and their finite times derivatives and attenuate input disturbances in any desired accuracy.…”

Fault detection and isolation for discrete-time Markovian jump systems with generally bounded transition probabilities: A zonotope-based method

“…Up to now, various methods on the fault diagnosis have been proposed for different systems (Edwards et al, 2000;Han et al, 2019b;Hwang et al, 2010;Li and Yang, 2014;Li et al, 2020;Li et al, 2019a;Naderi and Khorasani, 2017;Wang and Yang, 2020;Wang et al, 2007;Yeu et al, 2005;Zhang et al, 2019b;Zhu and Yang, 2013), but very few for MJSs. Exceptionally, some works have been conducted for MJSs (Chen et al, 2019;Dong et al, 2012;Dong et al, 2018;Han et al, 2019a;Li et al, 2018aLi et al, , 2018cLi et al, , 2018bLi et al, , 2019bLi et al, , 2019c;Liang et al, 2018;Wang et al, 2019;Yang et al, 2020;Zhang et al, 2019a;Zhong et al, 2005). For example, Li et al (2019b) proposed the simultaneous fault estimation method and non-fragile fault-tolerant control for MJSs.…”

“…Han et al (2019a) developed a reduced-order observer to provide the fault information, based on which the fault-tolerant control was discussed. Li et al (2019c) designed an adaptive observer to estimate the actuator fault under the consideration of actuator degradation. Chen et al (2019) also proposed an iterative adaptive observer to address the fault reconstruction problem.…”

“…On the one hand, Li et al (2019b); Han et al (2019a); Li et al (2019c); Chen et al (2019); Yang et al (2020); Liang et al (2018); and Li et al (2018b) addressed the fault estimation problems for some kinds of MJSs with access to more detailed fault information; however, they lost sight of the FDI issue, which is the main work of the paper. On the other hand, as stated in Dong et al (2012); Wang et al (2019); Zhang et al (2019a); Li et al (2018a); and Zhong et al (2005) effective fault detection observers were proposed for MJSs, where the thresholds were based on the residuals and tended to be constant after some time.…”