Observer-based optimal fault detection using PDFs for time-delay stochastic systems

被引:34
作者
Li, Tao [1 ]
Guo, Lei [1 ,2 ]
Wu, Lingyao [1 ]
机构
[1] Southeast Univ, Res Inst Automat, Nanjing 210096, Peoples R China
[2] Beihang Univ, Sch Instrument Sci & Oproelect Engn, Beijing 100083, Peoples R China
关键词
fault detection; stochastic system; B-spline expansion; probability density function; delay-dependent; LMI;
D O I
10.1016/j.nonrwa.2007.06.010
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper concerns the problem of fault detection (FD) for general stochastic systems with time delays. Different from the classical FD problem, the available information for the FD is the input and the measured output probability density functions (PDFs) of the system. Based on this, firstly, square root B-spline expansions technique is applied to model the PDFs so that the concerned FD problem is transformed into a nonlinear FD problem subject to the weight dynamical systems. Secondly, by using the FD observer as residual generator and guaranteed cost performance index as objective function, design of the FD observer is formulaled as an optimization problem. A delay-dependent condition to solve this problem is established in terms of the feasibility of linear matrix inequality (LMI). Moreover, in order to improve FD performance, the guaranteed cost algorithm is applied to optimal observer design. Finally, two examples are given to demonstrate the applicability of the proposed approach. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2337 / 2349
页数:13
相关论文
共 28 条
[1]  
[Anonymous], 2006, 2006 AM CONTR C
[2]  
Boyd S, 1994, STUDIES APPL MATH
[3]  
Chen J., 2012, Robust model-based fault diagnosis for dynamic systems, VVol. 3
[4]   Optimal stochastic fault detection filter [J].
Chen, RH ;
Mingori, DL ;
Speyer, JL .
AUTOMATICA, 2003, 39 (03) :377-390
[5]   Control of particle size distribution described by a population balance model of semibatch emulsion polymerization [J].
Crowley, TJ ;
Meadows, ES ;
Kostoulas, E ;
Doyle, FJ .
JOURNAL OF PROCESS CONTROL, 2000, 10 (05) :419-432
[6]   FAULT-DIAGNOSIS IN DYNAMIC-SYSTEMS USING ANALYTICAL AND KNOWLEDGE-BASED REDUNDANCY - A SURVEY AND SOME NEW RESULTS [J].
FRANK, PM .
AUTOMATICA, 1990, 26 (03) :459-474
[7]   Delay-dependent stability and H∞ control:: constant and time-varying delays [J].
Fridman, E ;
Shaked, U .
INTERNATIONAL JOURNAL OF CONTROL, 2003, 76 (01) :48-60
[8]   An improved stabilization method for linear time-delay systems [J].
Fridman, E ;
Shaked, U .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (11) :1931-1937
[9]   Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters [J].
Guo, L ;
Wang, H .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2005, 52 (08) :1644-1652
[10]   PID controller design for output PDFs of stochastic systems using linear matrix inequalities [J].
Guo, L ;
Wang, H .
IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS, 2005, 35 (01) :65-71