Fault detection for a class of non‐linear networked control systems in the presence of Markov sensors assignment with partially known transition probabilities

Abstract

In this study, the problem of fault detection for a class of discrete-time non-linear networked control systems is investigated. An event modelled as a Markov chain taking matrix values in a certain set with partially known transition probabilities is utilised to characterise the phenomenon of the sensors assignment. A full-order mode-dependent fault detection filter is constructed and the corresponding fault detection problem is converted into an H ∞ filtering problem of a Markov jump system with partially known transition probabilities. Sufficient conditions for the existence of the fault detection filter are formulated as a linear matrix inequality-based convex optimisation problem. If the convex optimisation problem has a feasible solution, the corresponding fault detection filter parameters are determined. A numerical example with four cases of transition probability matrices is presented to show the usefulness of the developed method. IntroductionThe last two decades have witnessed the extensive investigation on the so-called networked control systems (NCSs). Different from the traditional point-to-point control systems, the sensor, controller and actuator of NCSs are located in different places and linked via a wire/wireless communication channels. Therefore, NCSs have been widely used in many areas such as automobiles, manufacturing plants, aircrafts and so on since they bring a lot of advantages, for example, low cost, simple installation and maintenance, increased system agility and reduced weight and so on [1, 2]. However, owing to the limited bandwidth or capacity of the inserted communication network, NCSs also give rise to a set of issues, such as network-induced delays (or transmission delays), packet dropouts (or data missing), quantisation effects, scheduling schemes and fading problems, which inevitably lead to poor system performance or even instability. Recently, the problems of stability analysis and filtering design for NCSs with the effect of network-induced delays and packet dropouts have been paid on much more attention than before, see the recent overviews on NCSs [3, 4] and references therein.Most of literatures on NCSs have only concerned the most basic issues of network-induced delays and packet dropouts without considering the problems of others. In fact, a scheduling scheme or an activation management policy is also an important issue for NCSs and should not be ignored, especially for a large system with numerous sensors and actuators, which cannot be simultaneously accommodated by the network with limited bandwidth/capacity or limited power supply. Therefore the concept of communication sequence first was presented in [5], which investigated the network scheduling when some NCSs were linked to the network and with the assumption that the network bandwidth is arbitrary, meanwhile, it applies the rate monotonic scheduling algorithm to schedule a set of NCSs. And what follows, Walsh et al. [2] introduced the try-once-discard (TOD) protocol for multiple-input-multiple-output NCSs, whi...

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