Fault Detection for Linear Discrete Time-Varying Systems Subject to Random Sensor Delay: A Riccati Equation Approach

This paper mainly studies the fault detection (FD) problem for linear discrete time-varying systems subject to random sensor delay. By assuming that the measurement channel is with Transmission Control Protocol (TCP), an observer-based FD filter (FDF) is provided as a residual generator via embedding the packet indicator into the filter. To construct this FDF, its design issue is formulated into two sub-problems. One is to maximize the H-/H_∞ or H_∞/H_∞ FD performance index, which aims to enhance the ratio of fault sensitivity/disturbance attenuation. The other one is to find the filter parameter matrices such that the error between the residual and the fault is minimized in the H_∞ sense. By employing stochastic analysis and introducing some adjoint operator based optimization approaches, analytical solutions to the aforementioned FDF design problem are derived via solving recursive Riccati equations. An illustrative example is given to show the effectiveness of the proposed methodologies.

I. Introduction

In order to satisfy the increasing demands on safety and reliability for dynamic systems, much attention has been focused on fault detection (FD) technology in the past two decades [1]–[9]. Among the fruitful results, model-based FD methodology plays a key role and has been applied to various kinds of complex systems for both theoretical research and industrial applications [10]–[13]. An efficient tool for achieving model-based FD is the so-called fault detection filter (FDF) design scheme which generates a residual signal to illustrate whether a fault occurs. Generally speaking, combing with robust optimization techniques, the FDF design can be carried out via two approaches. The first one is to design FDF by maximizing sensitivity/robustness ratio criteria, see [1], [14]–[16] and the references therein. The second one is to minimize the norm of the error between the fault and the residual, see [17]–[19] and the related references.