Fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation

This paper considers the problem of robust H_∞ fault detection for a class of uncertain nonlinear Markovian jump stochastic systems with mode-dependent time delays and sensor saturation. We aim to design a linear mode-dependent H_∞ fault detection filter that ensures, the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed H_∞-norm level for all admissible uncertainties. By using the Lyapunov stability theory and generalised Itô formula, some novel delay-dependent sufficient conditions in terms of linear matrix inequality are proposed to guarantee the existence of the desired fault detection filter. Explicit expression of the desired mode-dependent linear filter parameters is characterised by matrix decomposition, congruence transformation and convex optimisation technique. Sector condition method is utilised to deal with sensor saturation, a definite relation of sector condition parameters with fault detection system robustness against disturbances and sensitivity to faults is put forward, and weighting fault signal approach is employed to improve the performance of the fault detection system. A simulation example and an industrial nonisothermal continuous stirred tank reactor system are utilised to verify the effectiveness and usefulness of the proposed method.     

Fault detection for networked control systems subject to quantisation and packet dropout

This article addresses the stochastic fault detection (SFD) problem in finite-frequency domain for a class of networked control systems (NCSs) with respect to signal quantisation and data packet dropout. Considering a logarithmic quantiser and Markovian packet dropout, the NCS is modelled as a Markov jump linear system (MJLS) with quantisation error. Further, a new definition of finite-frequency stochastic H _? index is given, which gives a measurement of sensitivity. Subsequently, sufficient conditions are derived to guarantee that the MJLS can achieve such a performance. By virtue of the obtained conditions, the fault detection filters (FDFs) are designed in finite-frequency domain, which are valid in characterising the disturbance attenuation performance and finite-frequency fault sensitivity performance. Finally, a simulation example is given to illustrate the method and its effectiveness.     

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman–Yakubovic–Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H_? and H_∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.     

Finite-frequency fault detection for two-dimensional Fornasini–Marchesini dynamical systems

This paper is concerned with the fault detection problem for two-dimensional (2-D) discrete-time systems described by the Fornasini–Marchesini local state-space model. The goal of the paper is to design a fault detection filter to detect the occurrence of faults in finite-frequency domain. To this end, a finite-frequency H_? index is used to describe fault sensitivity performance, and a finite-frequency H_∞ index is used to describe disturbance attenuation performance. In light of the generalised Kalman–Yakubovich–Popov lemma for 2-D systems and matrix inequality techniques, convex conditions are derived for this fault detection problem. Based on these conditions, a numerical algorithm is put forward to construct a desired fault detection filter. Finally, a numerical example and an industrial example are given to illustrate the effectiveness of the proposed algorithm.     

A stable fault detection observer design in finite frequency domain

This article addresses the stable fault detection observer design problem for linear time-invariant continuous-time systems in finite-frequency domain. The fault detection filter design is a synthesised optimal Luenberger observer that guarantees two requested performance indexes of fault sensitivity and stability. With the aid of generalised Kalman–Yakubovich–Popov lemma and increasing dimensions of slack variable matrix, the stability and H _? performance analysis of the closed-loop system with a fault detection observer has been translated into a convex linear matrix inequality (LMI) optimisation problem to avoid the complexity of system associated with weight functions. An iterative LMI algorithm has been presented for the fault detection observer design. The effectiveness of proposed approaches is demonstrated by two numerical examples.     

Zonotopic fault detection observer design for Takagi–Sugeno fuzzy systems

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed method.     

Unknown Input Observer-based Actuator and Sensor Fault Estimation Technique for Uncertain Discrete Time Takagi-Sugeno Systems

This paper presents an Unknown Input robust Observer (UIO) capable of simultaneously estimate both sensor fault and system states. The system is assumed to be discrete-time Takagi-Sugeno (T-S) Fuzzy with uncertainties. An augmented system is obtained from the dynamic fault model and original system. Afterward, a UIO is designed for the augmented system aiming at decoupling process disturbances. Its design is obtained by using an H_∞ optimization technique and developed to maintain the observer stable, reducing the non-decoupled process disturbances effect. The proposed method is validated by two numerical examples as it is compared to a regular UIO technique and the extended Kalman filter. Results show the proposed technique presents better performance when the dynamic system is not purely nonlinear even if the same tuning parameters are chosen. Although other techniques are not able to ensure the error limitation, the proposed one is capable of it even in nonlinear systems.

     

Fault detection for discrete piecewise linear systems with infinite distributed time-delays

In this paper, the fault detection problem is investigated for a class of discrete-time piecewise linear systems with external disturbances and infinite distributed time-delays. As a modelling framework, piecewise linear system often arise when piecewise linear components are encountered, such as dead-zone, saturation, relays and hysteresis. The time-delays are assumed to be infinitely distributed in the discrete-time domain. The aim of this paper is to detect the possible faults and to estimate the system state. For this purpose, firstly, stability analysis is given based on a piecewise smooth Lyapunov function. Afterward, an appropriate approach of fault detection and filter design problem is provided to achieve a satisfactory balance between the disturbances attenuation level γ and the sensitivity to the fault for piecewise linear systems. As a consequence, a sufficient condition is obtained in terms of the linear matrix inequalities such that, for all admissible infinite distributed time-delays and external disturbances, the system is guaranteed to be asymptotically stable and the residual is guaranteed to satisfy H_∞ filtering performance and fault detection performance. At last, a simulation example is provided to demonstrate the applicability and effectiveness of the fault detection filtering scheme proposed in this paper.     

Fault detection and isolation for discrete-time switched linear systems based on average dwell-time method

This article is concerned with the problem of fault detection and isolation (FDI) for discrete-time switched linear systems based on the average dwell-time method. The proposed FDI framework consists of a bank of FDI filters, which are divided into N groups for N subsystems. The FDI filters belonging to one group correspond to the faults for a subsystem, and generate a residual signal to guarantee the fault sensitivity performance for the subsystem, the fault attenuation performance for other subsystems and the disturbance attenuation performance for all subsystems. Different form employing the weighting matrices to restrict the frequency ranges of faults for each subsystem, the finite-frequency H _? performance for switched systems is first defined. Sufficient conditions are established by linear matrix inequalities (LMIs), and the filter gains are characterised in terms of the solution of a convex optimisation problem. Two examples are used to demonstrate the effectiveness of the proposed design method.     

Fault detection filter design for stochastic time-delay systems with sensor faults

This article considers the fault detection (FD) problem for a class of Itô-type stochastic time-delay systems subject to external disturbances and sensor faults. The main objective is to design a fault detection filter (FDF) such that it has prescribed levels of disturbance attenuation and fault sensitivity. Sufficient conditions for guaranteeing these levels are formulated in terms of linear matrix inequalities (LMIs), and the corresponding fault detection filter design is cast into a convex optimisation problem which can be efficiently handled by using standard numerical algorithms. In order to reduce the conservatism of filter design with mixed objectives, multi-Lyapunov functions approach is used via Projection Lemma. In addition, it is shown that our results not only include some previous conditions characterising H _∞ performance and H _? performance defined for linear time-invariant (LTI) systems as special cases but also improve these conditions. Finally, two examples are employed to illustrate the effectiveness of the proposed design scheme.     

ℋ︁∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis

This paper presents a scheme to design robust sliding mode observers(SMO) with ??_∞ performance for uncertain nonlinear Lipschitz systems where both faults and disturbances are considered. We study the necessary conditions to achieve insensitivity of the proposed sliding mode observer to the unknown input(fault). The objective is to derive a sufficient condition using linear matrix inequality(LMI) optimization for minimizing the ??_∞ gain between the estimation error and disturbances, while at the same time the design method guarantees that the solution of the LMI optimization satisfies the so‐called structural matching condition. The sliding motion affects only a part of the system through a novel reduced‐order sliding mode controller. Furthermore, the so‐called equivalent control concept is discussed for fault estimation. Finally, a numerical example of MCK chaos demonstrates the high performance of the results compared with a pure SMO. Copyright © 2010 John Wiley & Sons, Ltd.     

Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults

The goal of this paper is to describe a novel fault tolerant tracking control (FTTC) strategy based on robust fault estimation and compensation of simultaneous actuator and sensor faults. Within the framework of fault tolerant control (FTC) the challenge is to develop an FTTC design strategy for nonlinear systems to tolerate simultaneous actuator and sensor faults that have bounded first time derivatives. The main contribution of this paper is the proposal of a new architecture based on a combination of actuator and sensor Takagi-Sugeno (T-S) proportional state estimators augmented with proportional and integral feedback (PPI) fault estimators together with a T-S dynamic output feedback control (TSDOFC) capable of time-varying reference tracking. Within this architecture the design freedom for each of the T-S estimators and the control system are available separately with an important consequence on robust L ₂ norm fault estimation and robust L ₂ norm closed-loop tracking performance. The FTTC strategy is illustrated using a nonlinear inverted pendulum example with time-varying tracking of a moving linear position reference.     

<Emphasis Type="Italic">l</Emphasis><Subscript>∞</Subscript> Fuzzy filter design for nonlinear systems with missing measurements: Fuzzy basis-dependent Lyapunov function approach

In this paper, l _∞ fuzzy filtering problem is dealt for nonlinear systems with both persistent bounded disturbances and missing probabilistic sensor information. The Takagi–Sugeno (T–S) fuzzy model is adopted to represent a nonlinear dynamic system. The measurement output is assumed to contain randomly missing data, which is modeled by a Bernoulli distributed with a known conditional probability. To design the l _∞ fuzzy filter and guarantee tracking performance, the effect of the perturbation against persistent bounded disturbances is reduced by using the minimum l _∞ performance. By using the fuzzy basis-dependent Lyapunov function approach, a sufficient condition is established that ensure the mean square exponential stability of the filtering error. The proposed sufficient condition is represented as some linear matrix inequalities (LMIs), and the filter gain is obtained by the solution to a set of LMIs. Finally, the effectiveness of the proposed design method is shown via an example.     

Adaptive nonlinear observer for state and unknown parameter estimation in noisy systems

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H_∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.     

Robust adaptive fault‐tolerant control of uncertain linear systems via sliding‐mode output feedback

This paper is concerned with the robust adaptive fault‐tolerant compensation control problem via sliding‐mode output feedback for uncertain linear systems with actuator faults and exogenous disturbances. Mismatched disturbance attenuation is performed via H_∞ norm minimization. By incorporating the matrix full‐rank factorization technique with sliding surface design successfully, the total failure of certain actuators can be coped with, under the assumption that redundancy is available in the system. Without the need for a fault detection and isolation mechanism, an adaptive sliding mode controller, where the gain of the nonlinear unit vector term is updated automatically to compensate the effects of actuator faults, is designed to guarantee the asymptotic stability and adaptive H_∞ performance of closed‐loop systems. The effectiveness of the proposed design method is illustrated via a B747‐100/200 aircraft model. Copyright © 2014 John Wiley & Sons, Ltd.     

Sensor fault diagnosis of singular delayed LPV systems with inexact parameters: an uncertain system approach

In this paper, sensor fault diagnosis of a singular delayed linear parameter varying (LPV) system is considered. In the considered system, the model matrices are dependent on some parameters which are real-time measurable. The case of inexact parameter measurements is considered which is close to real situations. Fault diagnosis in this system is achieved via fault estimation. For this purpose, an augmented system is created by including sensor faults as additional system states. Then, an unknown input observer (UIO) is designed which estimates both the system states and the faults in the presence of measurement noise, disturbances and uncertainty induced by inexact measured parameters. Error dynamics and the original system constitute an uncertain system due to inconsistencies between real and measured values of the parameters. Then, the robust estimation of the system states and the faults are achieved with H_∞ performance and formulated with a set of linear matrix inequalities (LMIs). The designed UIO is also applicable for fault diagnosis of singular delayed LPV systems with unmeasurable scheduling variables. The efficiency of the proposed approach is illustrated with an example.