Network‐based fault detection for discrete‐time state‐delay systems: A new measurement model

In this paper, the fault detection problem is studied for a class of discrete-time networked systems with multiple state delays and unknown input. A new measurement model is proposed to account for both the random measurement delays and the stochastic data missing (package dropout) phenomenon, which are typically resulted from the limited capacity of the communication networks. At any time point, one of the following cases (random events) occurs: measurement missing case, no time-delay case, one-step delay case, two-step delay case, …, q-step delay case. The probabilistic switching between different cases is assumed to obey a homogeneous Markovian chain. We aim to design a fault detection filter such that, for all unknown input and incomplete measurements, the error between the residual and weighted faults is made as small as possible. The addressed fault detection problem is first converted into an auxiliary H∞ filtering problem for a certain Markovian jumping system (MJS). Then, with the help of the bounded real lemma of MJSs, a sufficient condition for the existence of the desired fault detection filter is established in terms of a set of linear matrix inequalities (LMIs). A simulation example is provided to illustrate the effectiveness and applicability of the proposed techniques. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[2]  Björn Wittenmark,et al.  Stochastic Analysis and Control of Real-time Systems with Random Time Delays , 1999 .

[3]  Asok Ray,et al.  An observer-based compensator for distributed delays , 1990, Autom..

[4]  Ping Zhang,et al.  Beobachtergestützte Überwachung vernetzter regelungstechnischer Systeme (Observer Schemes for Networked Control Systems) , 2004 .

[5]  Torsten Jeinsch,et al.  A unified approach to the optimization of fault detection systems , 2000 .

[6]  Ron J. Patton,et al.  Design of Fault Detection and Isolation Observers: A Matrix Pencil Approach , 1998, Autom..

[7]  Fuwen Yang,et al.  Robust finite-horizon filtering for stochastic systems with missing measurements , 2005, IEEE Signal Processing Letters.

[8]  Paul M. Frank,et al.  Issues of Fault Diagnosis for Dynamic Systems , 2010, Springer London.

[9]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

[10]  Fuwen Yang,et al.  Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements , 2006, IEEE Transactions on Signal Processing.

[11]  Ron J. Patton,et al.  An observer design for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[12]  Fuwen Yang,et al.  H∞ control for networked systems with random communication delays , 2006, IEEE Trans. Autom. Control..

[13]  Qiang Ling,et al.  Optimal dropout compensation in networked control systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[14]  James Lam,et al.  Stabilization of linear systems over networks with bounded packet loss , 2007, Autom..

[15]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[16]  Mo-Yuen Chow,et al.  Gain adaptation of networked DC motor controllers based on QoS variations , 2003, IEEE Trans. Ind. Electron..

[17]  R. Patton,et al.  Optimal filtering for systems with unknown inputs , 1998, IEEE Trans. Autom. Control..

[18]  Biao Huang,et al.  A new method for stabilization of networked control systems with random delays , 2005, Proceedings of the 2005, American Control Conference, 2005..

[19]  Johan Nilsson,et al.  Real-Time Control Systems with Delays , 1998 .

[20]  Daniel W. C. Ho,et al.  Variance-constrained filtering for uncertain stochastic systems with missing measurements , 2003, IEEE Trans. Autom. Control..

[21]  András Varga,et al.  Computation of Kalman decompositions of periodic systems , 2003, 2003 European Control Conference (ECC).

[22]  James Lam,et al.  New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems , 2005, IEEE Transactions on Signal Processing.

[23]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .

[24]  P.M. Frank,et al.  Fault detection of networked control systems with missing measurements , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[25]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

[26]  J. Geromel,et al.  Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems , 2002 .

[27]  Dong Yue,et al.  STATE FEEDBACK CONTROLLER DESIGN OF NETWORKED CONTROL SYSTEMS WITH PARAMETER UNCERTAINTY AND STATE‐DELAY , 2006 .

[28]  Steven X. Ding,et al.  Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems , 2007, Autom..

[29]  Hao Ye,et al.  Fault diagnosis of networked control systems , 2007, Annu. Rev. Control..

[30]  Daniel W. C. Ho,et al.  Robust filtering under randomly varying sensor delay with variance constraints , 2003, IEEE Transactions on Circuits and Systems II: Express Briefs.

[31]  Ron J. Patton,et al.  Input Observability and Input Reconstruction , 1998, Autom..

[32]  Linda Bushnell,et al.  Stability analysis of networked control systems , 2002, IEEE Trans. Control. Syst. Technol..

[33]  James Lam,et al.  An LMI approach to design robust fault detection filter for uncertain LTI systems , 2003, Autom..

[34]  Yongqiang Wang,et al.  Fault detection of networked control systems with limited communication , 2009, Int. J. Control.

[35]  H. Ye,et al.  Fault detection for Markovian jump systems , 2005 .

[36]  Heinz Schättler,et al.  Time-stamped model predictive control: an algorithm for control of processes with random delays , 2004, Comput. Chem. Eng..