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In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out.

In the past decade, networked control systems (NCSs) have attracted much attention owing to their successful applications in a wide range of areas for the advantage of decreasing the hardwiring, the installation cost, and implementation difficulties. Nevertheless, the NCS-related challenging problems arise inevitably due to the physical equipment constraints and the complexity and uncertainty of the external environment in the process of modeling or information transmission, which would drastically degrade the system performances. Such network-induced problems include, but are not limited to, missing measurements, communication delays, sensor and actuator saturations, signal quantization, and randomly varying nonlinearities. These phenomena may occur in a probabilistic way that are customarily referred to as the randomly occurring incomplete information. Note that, in the literature concerning systems and control, incomplete information usually refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities.

For several decades, nonlinear analysis and stochastic analysis are arguably two of the most active research areas in systems and control. This is simply because (1) nonlinear control problems are of interest to engineers, physicists, and mathematicians because most physical systems are inherently nonlinear in nature and (2) stochastic modelling has come to play an important role in many branches of science and industry as many real world systems and natural processes may be subject to stochastic disturbances. There has been rich literature on the general nonlinear stochastic control problems. A great number of techniques have been developed on filtering, control, and fault detection problems for nonlinear stochastic systems in order to meet the needs of practical engineering. Recently, with the development of networked control systems, the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information have become interesting and imperative yet challenging topics that have gained a great deal of research attention.

The focus of this paper is to provide a timely review on the recent advances of the analysis and synthesis issues for nonlinear stochastic systems with randomly occurring incomplete information. Most commonly used methods for modeling randomly occurring incomplete information are summarized. Based on the models established, various filtering, control, and fault detection problems with randomly occurring incomplete information are discussed in great detail. Such kind of randomly occurring incomplete information typically appears in a networked environment, which includes randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements, and randomly occurring quantization. Subsequently, latest results on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information are reviewed. Finally, some concluding remarks are drawn and some possible future research directions are pointed out.

The rest of this paper is outlined as follows. In Section

Accompanied by the rapid development of communication and computer technology, NCSs have become more and more popular for their successful applications in modern complicated industry processes, for example, aircraft and space shuttle, nuclear power stations and high-performance automobiles. However, the insertion of network makes the analysis and synthesis problems much more complex due to the randomly occurring incomplete information that is mainly caused by the limited bandwidth of the digital communication channel. The randomly occurring incomplete information under consideration mainly includes missing measurements, communication delays, sensor and actuator saturations, signal quantization, and randomly varying nonlinearities.

In practical systems within a networked environment, the measurement signals are usually subject to probabilistic information missing (data dropouts or packet losses), which may be caused for a variety of reasons, such as the high manoeuvrability of the tracked target, a fault in the measurement, intermittent sensor failures, network congestion, accidental loss of some collected data, or some of the data may be jammed or coming from a very noisy environment, and so forth. Such a missing measurement phenomenon that typically occurs in networked control systems has attracted considerable attention during the past few years, see [

Owing to the fact that time delays commonly reside in practical systems and constitute a main source for system performance degradation or even instability, the past decade has witnessed a significant progress on analysis and synthesis for systems with various types of delays, and a large amount of literature has appeared on the general topic of time-delay systems. For example, in [

However, most research attention has been centered on the

As is well-known, quantization always exists in computer-based control systems employing finite-precision arithmetic. Moreover, the performance of NCSs will be inevitably subject to the effect of quantization error owing to the limited network bandwidth caused possibly by strong signal attenuation and perturbation in the operational environment. Hence, the quantization problem of NCSs has long been studied and many important results have been reported in [

In practical control systems, sensors and actuators cannot provide unlimited amplitude signal due primarily to the physical, safety, or technological constraints. In fact, the actuator/sensor saturation is probably the most common nonlinearity encountered in practical control systems, which can degrade the system performance or even cause instability if such a nonlinearity is ignored in the controller/filter design. Because of their theoretical significance and practical importance, considerable attention has been focused on the filtering and control problems for systems with

It is well known that nonlinearities exist universally in practice and it is quite common to describe them as additive nonlinear disturbances that are caused by environmental circumstances. In a networked system such as the internet-based three-tank system for leakage fault diagnosis, such nonlinear disturbances may occur in a probabilistic way due to the random occurrence of network-induced phenomenon. For example, in a particular moment, the transmission channel for a large amount of packets may encounters severe network-induced congestions due to the bandwidth limitations, and the resulting phenomenon could be reflected by certain randomly occurring nonlinearities where the occurrence probability can be estimated via statistical tests. As discussed in [

For several decades, stochastic systems have received considerable research attention in which stochastic differential equations are the most useful stochastic models with broad applications in aircraft, chemical or process control system, and distributed networks. Generally speaking, stochastic systems can be categorized into two types, namely, internal stochastic systems and external stochastic systems [

As a class of internal stochastic systems with finite operation modes, the Markovian jump systems (MJSs) have gained particular research interests in the past two decades because of their practical applications in a variety of areas such as power systems, control systems of a solar thermal central receiver, networked control systems, manufacturing systems, and financial markets. So far, existing results about MJSs have covered a wide range of research problems including those for stability analysis [

For external stochastic systems, stochasticity is always caused by external stochastic noise signal and can be modelled by stochastic differential equations with stochastic processes [

In the past decade, sensor networks have been attracting increasing attention from many researchers in different disciplines owing to the extensive applications of sensor networks in many areas including surveillance, environment monitoring, information collection, industrial automation, and wireless networks [

In recent years, the distributed filtering problem for sensor networks has received considerable research interest and a lot of research results have been available in the literature, see, for example, [

It should be pointed out that, so far, most reported distributed filter algorithms for sensor networks have been mainly based on the traditional Kalman filtering theory that requires exact information about the plant model. In the presence of unavoidable parameter drifts and external disturbances, a desired distributed filtering scheme should be made as robust as possible. However, the robust performance of the available distributed filters has not yet been thoroughly studied, and this would inevitably restrict the application potential in practical engineering. Therefore, it is of great significance to introduce the

Unfortunately, up to now, the distributed nonlinear

In [

In [

Considering the case that the transfer function method cannot effectively deal with the nonlinear time-varying systems, a recursive matrix inequalities technique has been proposed in [

In [

By noticing that the aforementioned scheme cannot be applied to complex dynamic systems with transmission delay or state delay, in [

Considering the case that the occurrence of incomplete information in sensor network is more complex and severer, the studies in [

In [

In this paper, we have reviewed some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. Most commonly used randomly occurring incomplete information models have been summarized. Based on this, various filtering, control, and fault detection problems have been discussed. In addition, the various distributed filtering technologies over sensor networks have been given. Latest results on analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information have been surveyed. Based on the literature review, some related topics for the future research work are listed as follows.

The nonlinearities considered in the existing results have been assumed to satisfy certain constraints for the purpose of simplifying the analysis, thereby bringing a great deal of conservatism. It would be a promising research topic to analyze and synthesize the general nonlinear systems with randomly occurring incomplete information.

Another future research direction is to further investigate multiobjective

It would be interesting to investigate the problems of fault detection and fault tolerant control for time-varying systems with randomly occurring incomplete information over a finite time horizon.

A trend for future research is to generalize the methods obtained in the existing results to the control, synchronization, and filtering problems for nonlinear stochastic complex networks systems with randomly occurring incomplete information.

A practical engineering application of the existing theories and methodologies would be fault detection for petroleum well systems.

This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of Germany.