Robust Filtering For Uncertain Systems With Time-Varying Delay In Network Environment

The filtering problem has long been a significant and interesting problem in the con-trol and signal processing fields since1960s. Control Science has been greatly promoted by the filtering theory, since by designing the proper filter estimating the variables that cannot be measured precisely, a great deal of control approaches based on unmeasured state variables have found a wide range of applications, such as navigation, target track-ing, control of vehicles, aerospace, and time series econometrics. With the development of modern industry, much higher demand is required for the control systems in cost, reli-ability, and maintainability. Meanwhile, following the developments of computing theory and technology, it has been noted that networked control systems (NCSs) possess many great advantages over traditional systems, such as low coat, reduced weight and pow-er requirements, facilitated system diagnosis and maintenance, improved flexibility and suppleness, and high reliability. Though NCSs have found successful applications in large amount of modern scientific areas such as internet-based control and filtering, distributed communication and industrial automation, etc, many unexpected phenomena may appear since the signal transmission is based on digital communication channels with limited capacity. Among these phenomena, the most important are measurement quantization, signal transmission delay, and data packet dropout. Most of these phenomena are caused by the missing information of signals measured and transmitted in a network environ-ment, which could lead to the poor performance and even instability of the systems. In this sense, many traditional approaches meet difficulties when developed to NCSs, which leads to that a great deal of issues with limited capacity channel are rather cutting-edge and challenging.This thesis aims to model the stochastic phenomena in a network environment, such as signal quantization, transmission delay, and packet dropout, in a more general way, ad-dresses some new issues, and propose new approaches to solve the robust filtering prob-lems for some common systems in practical engineering, such as linear system, Markov jump system, and fuzzy system. By transforming the filtering error system into an input-output form consisting two interconnected subsystems via a two-term approximation to the state delay variables, sufficient conditions, under which the filtering error system is stochastically stable with a prescribed c level are established based on the Scaled Small Gain (SSG) theorem developed for stochastic systems. The fault detection filtering issue for a class of discrete system with network-induced nonlinear characteristics subject to limited communication capacity is also taken into account as an important application of method proposed in this thesis, which is successfully applied to the fault detection problem of the continuous-stirred tank reactor (CSTR) demonstrating effectiveness of the proposed method.Chapters1and2summarize the background and existing results on the robust fil-tering problems, and investigate the H∞filtering problem for linear discrete systems with time-varying delays. By employing a two-term approximation for delayed state variables, in which both the lower and upper delay bounds are considered, the original system is transformed into an input-output form of interconnection of two subsystems. Based on the analysis of SSG of each subsystem, respectively, sufficient conditions, under which the filtering error system is asymptotically stable with a prescribed H∞performance level is presented. Chapter2offers deeper insights into the differences and connections between the input-output approach and the Lyapunov stability theory, and elaborates the way to reduce the conservatism. By comparison with other existing results, the method proposed in Chapter2is illustrated to have much less conservatism. The studies of this part provide vital reference for the solution of filtering problems for complicated stochastic systems with limited communication capacity, and has practical meanings for many NCSs.Chapters3and4focus on the robust filtering problems for another important sys-tems widely used in a great number of practical engineering, Markov jump systems with time-varying delays. Since the SSG theorem can not be employed to stochastic systems directly, Chapter3first developed the input-output research framework to the stochastic systems, based on which a model transformation with less conservatism by two-term ap-proximation to the delayed variables is applied and the obtained subsystems are analyzed, respectively. Then, new conditions for the existence of the H∞filter are established and the corresponding filter design method is proposed. Furthermore, Chapter4addresses the H∞filtering problems for the time-delay Markov jump systems subject to intermittent measurements and sensor saturation. The communication channel between the plant and the filter is supposed to be imperfect, and a Bernoulli process is employed to model the phenomenon of the missing measurements. By using a basis-dependent Lyapunov func-tion approach, sufficient conditions for the existence of the robust filters are established. Based on the conditions, the effects of sensor saturation and random noise depending on state and external-disturbance are also taken into account. The characteristic of sensor saturation is handled by a decomposition approach which is more general than those in the existing work where the sensor saturation and network-induced phenomenon were considered separately. Then, a full-order filter is designed by employing the incomplete output measurements such that the dynamics of the estimation error is guaranteed to be stochastically stable. The study of this part provides theoretical basis for filter design issues for a large quantity of practical control systems working under complicated condi-tions and switched mode.Considering network-based technology are widely applied in more and more indus-try areas including intelligence control systems, Chapter5investigates the H∞filtering problems for time-delay Takagi-Sugeno (T-S) fuzzy systems with quantization and in-termittent measurements. The communication links between the plant and filter are un-reliable network channels, and the effects of output logarithmic quantization and data packet losses are considered together. After modeling the network-induced phenomena, a systemic design approach is developed to design a robust filter such that the asymptotic estimates of system states is obtained by employing the incomplete output measurements. Sufficient condition is proposed such that the derived filtering error system is robustly stochastically stable with a prescribed disturbance attenuation level. Moreover, based on the research, another important nonlinear characteristic, sensor saturation is taken into consideration. With the help of decomposition approach, the robust filtering problem of sensor saturation is solved in a network environment and holds the application value for networked-based filtering systems in practical engineering.In Chapter7, Fault detection issue is addressed for a class of linear discrete system based on unreliable communication links. In the network communication channel, the ef-fects of signal quantisation, transmission delay, and measurement missing, which appear typically in a network environment, are taken into consideration simultaneously. In order to track the fault signal using the residual signal, a weighted fault signal is generated by employing a given stable weighting matrix. This linear weighting matrix realization has been widely used in the existing literature. After the evaluation of the generated residual via choosing the appropriate threshold, the logical relationship for fault detection is re-vealed. Based on modeling the network-induced characteristics, respectively, the focus is on the conditions, under which the residual generation system is stochastically stable and satisfies a prescribed disturbance attenuation level. By developing the linearization of the proposed conditions, a robust fault detection filter with less conservative is designed and applied in an industrial continuous-stirred tank reactor (CSTR). This part applies the fault detection filter design method to practical engineering systems, which extends the ideas of solving filtering problem for stochastic systems subject to multiple networked-induced nonlinearities, and presents an successfully example for the applications of robust filtering approaches.