Recursive State and Random Fault Estimation for Linear Discrete Systems under Dynamic Event-Based Mechanism and Missing Measurements

Xuegang Tian,Shaoying Wang,Pietro De Lellis

doi:10.1155/2020/5825341

Abstract

This paper is concerned with the event-based state and fault estimation problem for a class of linear discrete systems with randomly occurring faults (ROFs) and missing measurements. Different from the static event-based transmission mechanism (SETM) with a constant threshold, a dynamic event-based mechanism (DETM) is exploited here to regulate the threshold parameter, thus further reducing the amount of data transmission. Some mutually independent Bernoulli random variables are used to characterize the phenomena of ROFs and missing measurements. In order to simultaneously estimate the system state and the fault signals, the main attention of this paper is paid to the design of recursive filter; for example, for all DETM, ROFs, and missing measurements, an upper bound for the estimation error covariance is ensured and the relevant filter gain matrix is designed by minimizing the obtained upper bound. Moreover, the rigorous mathematical analysis is carried out for the exponential boundedness of the estimation error. It is clear that the developed algorithms are dependent on the threshold parameters and the upper bound together with the probabilities of missing measurements and ROFs. Finally, a numerical example is provided to indicate the effectiveness of the presented estimation schemes.

Highlights

To maintain the safety and reliability of actual systems, in the past decade, fault detection and fault estimation problems have become hot research topics, and plenty of results could be found in [12, 40,41,42,43,44,45,46,47]
It is worth mentioning that the faults are taken as constants in most cases; the practical engineering systems are usually suffered from unpredictable parameter fluctuations or sudden structural changes, so the time-varying and random characteristics of faults should be considered in the engineering reality [48, 49]. When it comes to the fault estimation issue in the networked control systems, randomly occurring faults (ROFs) has not yet gained attention, let alone the case where dynamic event-based mechanism (DETM) and missing measurements are taken into account
The dynamic eventbased state and fault estimation problem for linear discrete systems subject to missing measurements and ROFs is studied in this paper

Summary

Problem Formulation

Consider the following linear discrete systems with ROFs and missing measurements:. yi ΛiMixi + vi, where xi ∈ Rn is the state vector, yi ∈ Rm is the measurement output, and fi represents fault signal. The event-triggered condition of DETM satisfies the following relation:. The following event-based estimator is designed to simultaneously estimate state and fault for system (8): X􏽢 i+1|i HiX􏽢 i|i, X􏽢 i+1|i+1 X􏽢 i+1|i + Ji+1􏼐y􏽥i+1 − Mi+1X􏽢 i+1 | i􏼑,. We define the prediction error and its error ctEX􏽢ho[iev+X􏽥a1|rii+c+iao11n|raircXn􏽥eesdTip+O1o|nii+]ad1,si|irn+eg1sp≜eXe􏽥Ecrti[r+ioXv1􏽥r|eiil+≜y1.c|XoSi+vii1+maX1􏽥rii−lTia+an1rX􏽢l|cyiei+,+11t]|hia.erefieltaXeo􏽥nrbiid+nje1g|ci+tei1vr≜OerooXir+f1iat+|ihn1≜i−ds paper is to design time-varying estimator (10) such that there exist an array of positive-definite matrices Υi+1|i+1 satisfying Oi+1|i+1 ≤ Υi+1|i+1. In order to better reflect the engineering practice, the faults considered here can dynamically change and their dynamic characteristics are described in (3) Such a description has been widely adopted in the existing literature (see [48,49,50]). As stated in [34], if the dynamic variable εi satisfies (5), the triggering instants under DETM are smaller than the static status. The boundedness of the estimation error will be discussed in the sequel

Main Results

Performance Analysis

Illustrative Examples