A novel approach to fault detection for fuzzy stochastic systems with nonhomogeneous processes

In this paper, we consider a class of fuzzy stochastic systems with nonhomogeneous jump processes. Our focus is on the design of a fuzzy fault detection filter that is sensitive to faults but robust against unknown inputs. Furthermore, the error filtering system is stochastically stable. With reference to an H1 performance index and a new performance index, sufficient conditions to ensure the existence of a fuzzy robust fault detection filter are derived. Simulation studies are carried out, showing that the proposed fuzzy robust FD filter can rapidly detect the faults correctly

Filtering for discrete-time nonhomogeneous Markov jump systems with uncertainties

This paper studies the problem of robust H1 filtering for a class of uncertain discrete-time nonhomogeneous Markov jump systems. The time-varying jump transition probability matrix is described by a polytope. By Lyapunov function approach, mode-dependent and variation-dependent H1 filter is designed such that the resulting error dynamic system is stochastically stable and has a prescribed H1 performance index. A numerical example is given to illustrate the effectiveness of the developed techniques

Asynchronous switching control for fuzzy Markov jump systems with periodically varying delay and its application to electronic circuits

This article focuses on addressing the issue of asynchronous H∞ control for Takagi-Sugeno (T-S) fuzzy Markov jump systems with generally incomplete transition probabilities (TPs). The delay is assumed to vary periodically, resulting in one monotonically increasing interval and one monotonically decreasing interval during each period. Meanwhile, a new Lyapunov-Krasovskii functional (LKF) is devised, which depends on membership functions (MFs) and two looped functions formulated for the monotonic intervals. Since the modes and TPs of the original system are assumed to be unavailable, an asynchronous switching fuzzy controller on the basis of hidden Markov model is proposed to stabilize the fuzzy Markov jump systems (FMJSs) with generally incomplete TPs. Consequently, a stability criterion with improved practicality and reduced conservatism is derived, ensuring the stochastic stability and H∞ performance of the closed-loop system. Finally, this technique is employed to the tunnel diode circuit system, and a comparison example is given, which verifies the practicality and superiority of the method

A Novel Case of Practical Exponential Observer Using Extended Kalman Filter

This technical note presents a case of practical exponential observer using extended Kalman filter (EKF) independent of certain restrictions, such as online check and estimation error of initial state. Recursive state estimation is usually a challenge for discrete-time nonlinear system in terms of computation cost. EKF is attractive with its simplicity since it is considered as an exponential observer given the above restrictions. However, those restrictions are so mathematically complicated that EKF cannot be practical in estimation. A novel case for an exponential observer using EKF is proposed, which is independent of such restrictions. However, these restrictions are proved to be unnecessary in the case. The proposed case is illustrated by a navigation system scenario. The validity of the case is demonstrated by a numerical simulation experiment. The system is deterministic

Generalised criteria on delay dependent stability of highly nonlinear hybrid stochastic systems

Our recent paper [2] is the first to establish delay dependent criteria for highly nonlinear hybrid stochastic differential delay equations (SDDEs) (by highly nonlinear we mean the coefficients of the SDDEs do not have to satisfy the linear growth condition). This is an important breakthrough in the stability study as all existing delay stability criteria before could only be applied to delay equations where their coefficients are either linear or nonlin- ear but bounded by linear functions (namely, satisfy the linear growth condition). In this continuation, we will point out one restrictive condition imposed in our earlier paper [2]. We will then develop our ideas and methods there in order to remove this restrictive condition so that our improved results cover a much wider class of hybrid SDDEs

Fault detection filter and fault accommodation controller design for uncertain systems

Model-based Fault Detection (FD) and Fault Accommodation (FA) approaches have been applied in a variety of cases. We propose several techniques to include uncertainties in the design process. First, we focus on the design of the Fault Detection Filter (FDF) and Fault Accommodation Controller (FAC) for Markovian Jump Linear Systems (MJLS). The MJLS framework allows us to include the network behavior (packet loss) during the design of the FDF and FAC.Second, we propose an FDF and FAC design for the MJLS, under the assumption that the Markov chain mode is not directly accessible. Since we are using the MJLS framework to model the network behavior, the assumption that the network state is not instantly accessible is useful because from a practical standpoint this is a truthful assumption. Third, from the results presented for the MJLS framework, we provided follow-up results using Lur'e Markov Jump System. This is compelling since on some occasions the non-linear behavior cannot be ignored. Therefore, applying the Lur'e MJS framework allows us to consider the same assumptions from MJLS, but now adds the non-linearities. Fourth, we propose the design Gain-Scheduled FDF and FAC for Linear Parameter Varying (LPV) systems, under the assumption that the schedule parameter is not directly acquired. We assume that the schedule parameter is subject to additive noise. This imprecision is included during the design, using change of variables and multi-simplex techniques. Finally, throughout the thesis, we provide some numerical examples to illustrate the viability of the proposed approaches