Filter design, fault estimation and reliable control for networked time-varying systems: a survey

ABSTRACT This paper is concerned with the overview of the recent progress in filter design, fault estimation and reliable control for networked time-varying systems (NTVSs). Firstly, the concepts of the NTVS, incomplete information, filtering, estimation and control have been introduced. Secondly, the incomplete information phenomena are considered include, but not limited to, communication delays, measurement losses, actuator/sensor faults, signal quantizations and randomly occurring uncertainties. Subsequently, the developments as well as some recent results on filter design, fault estimation and reliable control are reviewed for NTVSs subject to incomplete information in great detail. Finally, conclusions are given and some possible future research directions are pointed out concerning the filtering, estimation and control problems.


Introduction
In the last decades, the progress of computers and communication network technology has a vital impact on the applications of control systems. However, due to the increasing complexity of the controlled plants, the control systems start to develop toward a more decentralized and intelligent direction, accordingly, the traditional point-topoint structure of control systems has been replaced by the private or public networks which can undertake the main transmission task through the components including sensors, controllers and actuators that distributed in different areas. Generally, when there exists a closed-loop control via a communication channel, the controlled systems can be called networked control systems (NCSs) (Walsh, Ye, & Bushnell, 2002). NCSs have many merits over traditional control systems, such as less modularity, easy maintenance, low cost and high reliability. In virtue of its practicability and validity, NCSs are implemented in various fields, for example, in car automation, experimental facilities, medical industry, domestic robots, space exploration, aircraft, automobiles, military systems (Shen, Wang, Liang, & Liu, 2012;Dong, Wang, Chen, & Gao, 2012;Ogren, Fiorelli, & Leonard, 2004;Seiler & Sengupta, 2005;Ding, Wang, & Shen, 2014;Dong, Wang, Alsaadi, & Ahmad, 2015;Li, Shen, Liang, & Shu, 2015;Sheng, Zhang, & Gao, 2014;Montagner, Oliveira, & Peres, 2006), and so on. On the other aspect, CONTACT Hongli Dong shiningdhl@vip.126.com it is worth noting that virtually most of the practical engineering systems are time-varying due to that the system parameters are definitely dependent on time, however, such time variations of parameters may result in considerable complexities in the system analysis and synthesis. For this reason, the networked time-varying systems (NTVSs) have become an increasingly hot research field.
Give some examples, in Sun, Xie, Xiao, & Soh (2008), Sun (2009), Sun & Xiao (2013) and Shu, Zhang, Shen, & Liu (2016), estimation, filtering and control problems have been investigated for linear discrete NTVSs with random measurement delays or packet dropouts or both. During the analysis process of NCSs, there is another issue that can not be ignored, that is, the unavoidable incomplete information phenomenon which would seriously degrade the system performance. Two sorts of factors would bring about this phenomenon strikingly. Firstly, the inherent characteristics of the NCSs such as large scale, multiple components, high complexity and wide distribution may lead to higher probabilities of the occurrence of faults in networked systems than in traditional systems. Secondly, since the network is a dynamic system, its quality of service depends on many factors, for example, bandwidth capacity, cable quality and so on. So if the phenomena such as cable aging, interface failures, limited bandwidth and network congestion arise, they will bring negative influences on the application service of networked systems. For the reasons given above, there is no doubt that the incomplete information phenomenon of NCSs has attracted unprecedented interests in recent years. In this paper, an introduction will be given about the incomplete information phenomena which include communication delays, measurement losses, actuator/sensor faults, signal quantizations and randomly occurring uncertainties.
As is known to all, as one of the fundamental problems, filter design problem has received considerable attention in signal processing and control engineering (Basin, Maldonado, & Karimi, 2011;Basin, Loukianov, & Hernandez-Gonzalez, 2013), and a great many of approaches including Kalman filtering, robust filtering, recursive filtering, H ∞ filtering, gain-scheduling filtering and optimal filtering (Shen, Wang, Shu, & Wei, 2010;Dong, Wang, & Gao, 2010;Hu, Wang, Shen, & Gao, 2013b;Singer, 1970;Shi, Fang, & Yan, 2009;Wang, Liu, Liu, Liang, & Vinciotti, 2009;Wei, Wang, Shen, & Li, 2011;Liu, Wei, Song, & Liu, 2016;Wen, Cai, Liu, & Wen, 2016) have been applied in diverse systems such as uncertain time-delay systems (Wang, Yang, Ho, & Liu, 2006), stochastic systems (Wang et al., 2008) and nonlinear systems (Lam et al., 2005). The overall ideology of filtering problem is to form a type of best estimate for the real value of some certain system based on some potentially noisy observed values (Gao, Meng, & Chen, 2008;Gao, Lam, & Wang, 2005;Gao, Lam, Xie, & Wang, 2005;Meng, Lam, & Fei, 2009;Zhang, Xia, & Shi, 2009). On another research aspect, it is familiar to us that our methods and technologies used in classical or modern control system design are almost under the ideal situation that all system actuators and sensors are in good working conditions. Nevertheless, a number of control systems designed utilizing traditional techniques are unable to satisfy the required performance in the presence of actuator faults, sensor faults and component faults. Even worse, faults would appear at any time in the actual operation of the system, which may generate abnormal production and even make the entire production process stop. Consequently, we must improve the reliability and security of the system to ensure the production process to operate in a safe, reliable and efficient manner. Based on the issues above, the essential problem needs to be settled firstly is to estimate the shapes and sizes of faults (Zhang, Ning, & Shi, 2015;Zhang, Zhuang, & Braatz, 2016). After that, in order to maintain the ideal performance, the reliable control is necessary especially in safety-critical systems which should tolerate failures in system components, such as military space mission, aircrafts, nuclear reactors, etc. The study of the design of reliable control systems has gained much attention in the early years, see e.g. Ackermann (1984), Veillette, Medanic, & Perkins (1992) and Vidyasagar & Viswanadham (1985).
Motivated by the above discussions, we aim to timely review the latest progress of the filter design, fault estimation and reliable control problems for NTVSs with incomplete information phenomena. The analysis and synthesis problems of the NTVSs are reviewed firstly. In the same part, the concepts of filter design, fault estimation and reliable control are introduced. Secondly, the recent developments of incomplete information consisting of communication delays, measurement losses, actuator/sensor faults, signal quantizations and randomly occurring uncertainties are discussed. Thirdly, latest results on filter design, fault estimation and reliable control approaches for NTVSs with incomplete information are surveyed in great detail. Finally, conclusions are drawn and some related directions for the further research are pointed out.
The remainder of this paper is organized as follows. In Section 2, the incomplete information phenomena are discussed. In Section 3, the developments of the filter design, fault estimation and reliable control problems for NTVSs with incomplete information are reported. The conclusions as well as some future research topics are presented in Section 4.

Incomplete information phenomena
Over the past ten years or so, adequate attention has been paid on the problems of incomplete information focusing on the communication delays, measurement losses, actuator/sensor faults, signal quantizations, randomly occurring uncertainties, etc.

Communication delays
The communication delays prevalently reside in practical systems, which result from the limited speed of information processing or finite switching speed of amplifiers (Liang, Wang, & Liu, 2010;Hu, Chen, & Du, 2014;Yin, Luo, & Ding, 2014;Liang & Cao, 2007;Zhang, Liu, Fang, & Chen, 2013;Liu, Wang, Zhu, & Liu, 2014). According to the different ways of occurring, delays have been classified into different types, including discrete delays, distributed delays, constant delays and timevarying delays. Owing to the universality and complexity of the time delays, it is significant and challenging to design effective algorithms so as to reduce the impacts from delays on the NCSs. Recently, many efficient methods have been proposed to reduce the conservatism induced by the time delays, for instance, the slack matrix variables technique (Wu et al., 2004), the bounding technique (Moon, Park, Kwon, & Lee, 2001), the descriptor system method (Fridman & Shaked, 2002) and the delay-fractioning approach (Peaucelle, Arzelier, Henrion, & Gouaisbaut, 2007;Hu, Wang, Gao, & Stergioulas, 2012b), see Hu, Wang, Chen, & Alsaadi (2016) for detail. It should be pointed out that researchers have a passion for the delay-fractioning approach, because when the number of fractions increases or more computational complexity is introduced, the delay-fractioning approach is more efficient than other techniques or methods in reducing the conservatism ascribed to time delays. Fortunately, along with rapid evolution of the computer technology, the computational complexity problem is solvable. Nowadays, the reported delay analysis methods have motivated a lot of interesting researches and a large quantity of papers have been published. It is obvious that, the delays discussed before almost arises continuously, but the communication delays caused by network transmissions may occur stochastically. Accordingly, random communication delays have raised some preliminary concerns, for example, the estimation and filtering problems have been discussed for networked systems with random communication delays (Chen, Xu, & Du, 2016;Dong, Wang, & Gao, 2010;Han, Zhang, & Fu, 2013;Sun & Ma, 2014).

Measurement losses
In networked systems, the phenomenon of measurement losses occurs at a high frequency, and there are many reasons which would generate it. On one hand, the faults in measurement outputs, network jams and accidental sensor failure will result in the packet losses of measurement signals. As we all know, the traditional control, estimation and filtering algorithms assume that the measurement outputs are available all the time, which should be improved due to the possible measurement losses in practical engineering. On the other hand, reflection, refraction and diffraction are inevitable when the signal is transmitted over a wireless channel, and multiple path-induced fading or shadow fading will happen which may severely degrade the characteristic of the system. Based on the facts above, performance analysis and synthesis for networked systems have drawn public attention doubtlessly (Hu et al., 2013b). For instance, the Kalman filtering problem with intermittent observations has been investigated in Sinopoli et al. (2004). In Shu, Lam, & Xiong (2009), the missing data in actuators has been considered for studying the non-fragile exponential stability assignment of discrete-time linear systems. Moreover, the filtering and estimation problems with missing measurements have received high degree of attention, and a lot of research results have been reported (Dong, Wang, Ho, & Gao, 2010;Shen, Wang, & Hung, 2010;Gao & Chen, 2007;Sahebsara, Chen, & Shah, 2007;Wang, Yang, Ho, & Liu, 2005).

Signal quantizations
In the NCSs, quantizer is a device or algorithmic function for the sake of processing the signals which required to be quantized before transmission (Brockett & Liberzon, 2000;Dong, Wang, Ding, & Gao, 2015). Quantization is a process which converts a real-valued signal into a piecewise constant one taking on a finite set of values by the quantizer. There are several reasons which would impact the system behaviour caused by quantization. For one thing, if the signal is out of the range of the quantizer, then the control law designed for the ideal case may lead to instability of the system. The other one is the deterioration of performance near the equilibrium: it is worthwhile to mention that if the distinction between the current and the desired values of the state is small, higher precision is necessary, so asymptotic convergence performance of the system is impossible in this condition. Recently (2011) to deal with the quantization problems. Up to now, plenty of efforts have been devoted to solve the filtering and fault detection problems for networked systems with signal quantization, and some effective algorithms have been reported (Hu et al., 2013b;Li, Shi, Wang, & Agarwal, 2015;You et al., 2014). For example, in Li, Shi, et al. (2015), the fault detection problem has been addressed for networked control systems with Markovian packet dropouts as well as quantization.

Sensor saturations
In reality, the reason in breaking the high-performance promises of traditional filter theories is that the sensors of system cannot provide signals with unlimited amplitudes as the result of physical or technological constraints. The appearance of the sensor saturations not only limits the filtering performance, but also may lead to unexpected oscillatory behaviour or, even worse, instability of the NCSs. Therefore, the related control and filtering problems have attracted scholars' interests under sensor saturations, see e.g. Fridman & Dambrine (2009), Cao, Lin, & Chen (2003), Dong, Wang, & Gao (2012) and Ding, Wang, Shen, & Shu (2012). Now, the challenging task is to develop a filtering algorithm by making the utmost use of the available information about the sensor saturations to satisfy the required performance or constraints. Some original results have been reported, such as the sector-bounded approach has been considered to eliminate the effects of sensor saturations (Xiao, Cao, & Lin, 2004;Yang & Li, 2009). In addition, the decomposition technique has been utilized to promote the filter design for networked systems, for example, in Hu, Wang, Gao, & Stergioulas (2012b), concerning nonlinear time-varying systems with uncertain parameters and sensor saturations, the probability-guaranteed H ∞ finite-horizon filtering problem has been solved.

Randomly occurring uncertainties
It is generally known that uncertainties commonly exist in practical engineering systems, which are induced by environmental circumstances such as repairs of components and random failures, changing of subsystem interconnections and abrupt environmental disturbances, see Hu et al. (2012b) for detail. In fact, parameter uncertainties always occur in a probabilistic way and a stochastic variable obeying the given Bernoulli distribution can be utilized to account for such kind of phenomenon. This phenomenon can reflect parameter variations in a random way, especially in the network transmission. For example, in the NCSs, the uncertainties may take place according to the randomly changeable network conditions. Therefore, before designing the actual control systems, the random uncertainties should be taken into consideration as an important factor. Recently, in Zhang, Wang, Ding, & Shu (2014), the H ∞ fuzzy filtering problem has been investigated for a class of discrete-time Takagi-Sugeno fuzzy systems with randomly occurring uncertainties as well as channel fadings. In Hou, Dong, Bu, & Yang (2016) and Huo, Chen, & Shen (2017), the estimator has been designed for discrete neural networks with randomly occurring uncertainties and missing measurements, and the eventbased robust state estimation problem has been solved in Wang, Fang, & Tian (2017) for discrete time-varying system with uncertain observations and randomly occurring uncertainties. Moreover, to deal with the fault estimation issue with packet dropouts and randomly occurring uncertainties, the recursive approach has been proposed in Song, Hu, Chen, Ji, & Liu (2016).
From the points above, to establish a unified measurement model which reflects different kinds of incomplete information is significant in both theory and practice. However, solving the following identified problems has become a challenging task. First of all, how to comprehend the laws that these recognized phenomena should comply with when they really occur? Then, how can we identify and define the most common type of incomplete information phenomena that occur in the NTVSs? Besides, how to choose a suitable mathematical expression to construct a new measurement model which can describe the considered phenomena well and characterize their occurrence laws?

Filter design, fault estimation and reliable control for networked time-varying systems
In this part, the advances of the filter design, fault estimation and reliable control for NTVSs are systematically reviewed. Here, we emphasize some latest works, including estimation, filtering and control algorithms which have been put forward to reduce the influence of the incomplete information onto the ideal performance under various restrictions.

Design of various kinds of filter
Robust/H ∞ Filter Design. The past several years have witnessed the rapid progress and extensive applications of filtering in the real world, such as in spacecraft, navigation, digital image processing, remote sensing technology, signal denoising, target tracking and industrial monitoring, where the Kalman filter is widely deployed. It is worth mentioning that the Kalman filtering approach can be executed only under the assumption that all noise terms and measurements own known distributions and an accurate knowledge of the underlying linear system model is available. However, it is hard to provide the ideal condition under the effects of measurement noises, modelling errors, parameter uncertainties and external disturbance. In this case, the robust/H ∞ performance of the networked systems has been paid adequate research attention due to its engineering significance. To mention a few, in Feng, Wang, & Zeng (2011), considering the linear time-varying systems, the robust non-fragile filtering problem has been addressed with multiple packet dropouts and a locally optimal filtering algorithm is established. Specially, in the minimum mean-square error sense, a globally optimal filtering scheme has been proposed in Li, Zhou, & Wu (2013) based on the result in Feng et al. (2011). In view of the missing measurements and quantization effects, the effective H ∞ filtering scheme has been presented in Wang, Dong, Shen, & Gao (2013). In addition, the filtering problems for nonlinear timevarying networked systems have come into our vision in parallel to the linear systems. For example, in Ding, Wang, Shen, & Dong (2015) and Guan, Fei, Li, & Xu (2016), the H ∞ filters have been constructed respectively for discrete time-varying networked systems with randomly occurring nonlinearities and fading measurements and with time-varying delays, and a further result of a probabilityguaranteed H ∞ finite-horizon filtering method has been reported in Hu et al. (2012b) for a class of time-varying nonlinear systems with sensor saturations.
Recursive Filter Design. In recent years, due to the inevitable nonlinearity problem of practical systems, the analysis and synthesis of nonlinear systems have become a very active research topic and some results have been published (Hu, Wang, & Gao, 2013;Hu, Wang, Shen, & Gao, 2013a). As mentioned in the last paragraph, the traditional Kalman filtering theory may not satisfy the required performance in the case that the system model is nonlinear even along with uncertainties. For the sake of improving its abilities of handling nonlinearities and uncertainties, many optional methods have been explored in the literature including the robust extended Kalman filter (Hu et al., 2013a;Kai, Wei, & Liu, 2010), H ∞ filtering Guan et al., 2016;Hu et al., 2012b), etc. Except for the methods above, the recursive filtering approach which can deal with this kind of problem has stirred an increasing research interest, and some latest results can be given in Feng et al. (2011) and Hu et al. (2013Hu et al. ( , 2013aHu et al. ( , 2013b and the references therein. In Hu et al. (2013a), the recursive filter has been designed for time-varying nonlinear systems encountering probabilistic sensor delays and finite-step correlated measurement noises. Furthermore, the recursive filter has been constructed for nonlinear time-varying networked systems with multiple missing measurements or quantization measurements. For example, the recursive filtering problem has been developed in Hu et al. (2013) for the nonlinear system with random parameter matrices, correlated noises and multiple fading measurements.
Gain-Scheduling Filter Design. It is not surprising that the gain-scheduling method, as one of the most effective ones for filter design problems of time-varying systems, has been paid more and more attention in the past decade (Hoang, Tuan, Apkarian, & Hosoe, 2004; Liu, Liu, & El Saddik, 2011;Luo, Wei, Karimi, & Wang, 2013;Wei et al., 2011). Its primary thought is to design filter gains as functions of the scheduling parameters, and the gains are assumed to be derived timely. The goal of utilizing parameter-dependent Lyapunov function related gainscheduling technique is to reduce the possible conservatism Gao, Meng, et al. (2008). Under guaranteed H 2 , H ∞ or mixed H 2 /H ∞ performance, the H 2 and H ∞ discretetime gain-scheduled filters have been designed in Hoang et al. (2004). An optimal gain scheduling approach has been presented in Liu et al. (2011) to select appropriate external scheduling gain from a deal of optimal gains obtained off-line for the NCSs with packet losses. Moreover, the probability-dependent gain-scheduling filtering problem has also been considered in Wei et al. (2011), and an elegant result has been derived for systems with missing measurements, while a robust H ∞ deconvolution filter has been constructed in Luo et al. (2013) to handle the randomly occurring sensor delays by the probabilitydependent method.
It is worth noting that the results of filters design for nonlinear time-varying NCSs with incomplete information are rarely reported compared with the linear ones, and it provides guiding references for future research.

Fault estimation for time-varying networked systems
In practical engineering, faults are undesirable deviations of system parameters from normal states, which are caused by unexpected model uncertainties, time delays, disturbances, perturbations and noises. As the unacceptable deviation will prevent the control system from achieving the desired performance, the fault detection and isolation (FDI) issues are of great significance and have received a wide range of attention, see, e.g.  (2010) and You et al. (2014). However, the difficulty encountered is to get the accurate size of the fault from a FDI scheme (Liu, Cao, & Shi, 2013). Therefore, the fault estimation issue is introduced to derive the size and shape of the faults and reconstruct the fault signals so as to perform the required fault detection automatically (Huang & Yang, 2014).
The key of fault estimation is to design a fault estimator. Regard the input signal and measurable output signal as the inputs of the estimator, and the output signal is the reconstructed fault estimation signal. Moreover, the reconstructed signal can be used as the input signal of the fault-tolerant controller to improve the faulttolerant performance of the system. Compared with the fault diagnosis method based on residual generation, the fault estimation one can better represent the severity of the fault. In recent years, many researchers in the fields of FDI have been devoted to explore effective fault estimators to obtain the on-line accurate fault information, and plenty of important results have been published. There exist some common methods of fault estimation, including adaptive observer (Li, Shi, Yao, & Wu, 2016), neural network (Zhou, Shi, Xu, & Li, 2013), T-S observer (Shen, Jiang, & Cocquempot, 2014), robust Kalman filter (Hu et al., 2013b), sliding mode observer approach and H ∞ optimization method (Zhang, Jiang, & Shi, 2009;Yan & Edwards, 2007Zhang, Swain, & Nguang, 2014;Shen, Steven, & Wang, 2013), and some other excellent fault estimation approaches have been shown in the literature (Park, 2010;Yao, Qin, Wang, & Jiang, 2012;Rodrigues, Hamdi, Theilliolet, Mechmeche, & BenHadj Braiek, 2015;Zhang, Jiang, & Staroswiecki, 2010;. In regard to the fault estimation problem for timevarying systems, some efforts have been made to design fault estimators on a finite time-horizon accompanying with incomplete information. For example, the estimation problems of randomly occurring faults over a finite horizon have been handled in Dong, Wang, Ding, & Gao (2014) for systems with different sources of disturbances via the recursive Riccati difference equation approach, while the recursive matrix inequality method has been utilized in Dong, Wang, Ding, & Gao (2016) to deal with the estimation problem. As is well known, the nonlinearities and uncertainties may make the system modelling complex, therefore, it is necessary to tackle them carefully when analysing the complex dynamical systems under increasing performance requirements (Basin et al., 2013;Ding, Wang, Alsaadi, & Shen, 2015;Ding, Wang, Lam, & Shen, 2015;Dong et al., 2014;Ma, Wang, Lam, Alsaadi, & Liu, 2016). For instance, the fault signal has been estimated in Dong et al. (2014) for a class of time-varying systems with stochastic nonlinearities, and it can be seen that a novel performance requirement against different sources of disturbances has been introduced. Especially mentioned, for the purpose of receiving less conservative results as well as computationally attractive algorithms, the Krein-space approach has been introduced to deal with the finite-horizon fault estimation problems and this method has been proven to be an effective tool to solve the filtering problems with the performance index described by an indefinite quadratic form. To list a few, in Zhong et al. (2010), the H ∞ fault filter has been constructed for linear discrete time-varying systems by using the Krein-space theory. Moreover, in Shen, Ding, & Wang (2013), the measurement delays have been taken into consideration, and a finite-horizon H ∞ fault estimator has been obtained with the help of the Kreinspace theory. The robust H ∞ fault estimation problem has been addressed in Shen, Steven, et al. (2013) in the framework of Krein spaces.
Unfortunately, up to now, the fault estimation for nonlinear time-varying NCSs with randomly occurring incomplete information has gained very little research attention despite its practical importance.

Reliable control for networked time-varying systems
In practical control systems especially NCSs, intolerable system performance will appear due to a variety of reasons (changes of working conditions, sensors or actuators aging, zero shift, electromagnetic interference and network disturbance) (Yue, Lam, & Ho, 2003). Therefore, it is practically crucial to design a controller to remain the stability of the system and ensure the system to run properly even the failure exists. Reliable control refers to that no matter there is a failure or not, a controller can always be designed to keep the system stable and meeting certain performance requirements. In recent years, the development of control system is more and more complex, thus enhancing the reliability has attracted public concerns.
Over the past several decades, different methods have been presented so as to satisfy various performance requirments. In Veillette et al. (1992), a methodology has been developed for the design of reliable centralized and decentralized control systems, which meets the H ∞ performance under the conditions not only when all control components are operational, but also when there are sensor or actuator outages in the centralized case or control channel outages in the decentralized case. After that, a procedure has been put forward for the design of reliable linear-quadratic state-feedback controller which guarantees the system stable and a known quadratic performance bound (Veillette, 1995). In addition, a method based on the Hamilton-Jacobi inequality approach has been presented for the design of reliable nonlinear control systems and the H ∞ performance has been taken into account in Yang, Lam, & Wang (1996). In terms of the linear matrix inequality approach, a method has been proposed for designing a reliable fuzzy controller in Chen & Liu (2004) in the sense of asymptotic stability, and the received controller is suitable for the systems whose control components are operating well or in fault.
Along with the methods proposed, a rich body of relevant literature subject to incomplete information or faults issues have been published, see e.g. Gao, Breikin, & Wang (2008), Tian, Yue, & Peng (2010), Tian, Yue, Yang, Gu, &Lu (2011) andZhang, Su, Pan, Chu, &. The reliable H ∞ control problem has been investigated for discrete-time linear time-varying systems in view of the admissible infinite distributed delays and possible actuator failures in Wang, Wei, & Feng (2009), ensuring that the closed-loop system is exponentially stable with a given disturbance attenuation level γ . In Tian et al. (2010), the proposed reliable controller has been designed for NCSs with undergoes probabilistic actuator fault, measurements distortion, random network-induced delay and packet dropout. Lately, as a newly emerged research topic, the finite-horizon reliable H ∞ output feedback control problem has been raised for a class of discrete time-varying systems in Dong, . The main idea is to design a time-varying output feedback controller over a given finite horizon such that, in the simultaneous presence of randomly occurring uncertainties, randomly occurring nonlinearities and measurement quantization, the closed-loop system achieves a prescribed performance level. In Liu, Gu, & Fei (2016), the reliable control problem has been settled for nonlinear systems with stochastic actuators fault and random delays via a T-S fuzzy model approach. It is worth mentioning that a novel state and sensor fault observer has been proposed in Gao, Breikin, et al. (2008) to estimate system states and sensor faults at the same time, where the considered sensor fault may be in any form, even in the unbounded one.
To the best of our knowledge, there exist only a few results on the reliable control for nonlinear time-varying complex systems with randomly occurring incomplete information, which still remains as a challenging research topic.
The following are some of the open problems that exist in most of the existing results. (1) As we all know, with regard to the designed filters or controllers for timevarying systems, we usually consider that the established filters or controllers are suitable as long as the designed gains are solvable. However, we are unable to give a sufficient condition for its feasibility and this has been an open topic for a long time.
(2) Note that, the parameters of time-varying system are variable with time and they are always just given by experience for simulations because we don't know the changing laws they frequently obey in real-world systems. This is another open problem.

Conclusions and future trends
In this paper, we have reviewed some recent advances on filter design, fault estimation and reliable control for NTVSs with incomplete information. Firstly, the analysis and synthesis of the NTVSs have been reviewed. Then, the developments of the incomplete information phenomena have been summarized. Based on these, the latest results on filter design, fault estimation and reliable control for networked time-varying systems with incomplete information have been surveyed. At last, based on the literature review, we give some related topics for the future research works as follows.
(i) Nowadays, the virtual reality technology has been one of the hot research fields, and it is worth considering the reliable control against equipment failure and environmental disturbance. (ii) Due to that communication protocols may prevent the data from collisions during the signal transmissions, it is a challenging direction to investigate filtering, estimation and control problems for networked time-varying systems with communication protocol. (iii) Since the security is a 'hard' performance index, the analysis in mean-square sense is more conservative for practical engineering. Therefore, the further meaningful work is to solve the security problems with probabilistic performance index in the presence network attacks.
(iv) With the developments of technology, the deep neural network has attracted our attention, furthermore, from the aspect of engineering application, the security issue is critical. Therefore, exploring the fault detection and estimation problem for deep neural networks will be a significant task. (v) An additional trend for future research is to discuss the applications of the established theories and methodologies to some practical engineering problems such as power systems and artificial intelligence systems.

Disclosure statement
No potential conflict of interest was reported by the authors.