Recursive Filtering For Two-Dimensional Systems With Network-Induced Complexities

The filtering issue of two-dimensional(2-D)systems is one of the frontier research topics in control community.By using the available measurements,the main idea of filtering scheme is focused on designing effective filters to estimate the unavailable system states or restore the real signals contaminated by noises.Unlike the traditional one-dimensional(1-D)state-space models whose dynamic behaviors only evolve along one direction(the time axis),2-D systems possess two mutually independent evolutionary processes.Thanks to such an inherent feature,2-D systems have promising application potentials in image processing,seismic data processing,multi-variable network implementation,environmental monitoring,chemical process and other fields.However,the essential characteristic of bidirectional evolution also makes the analysis and synthesis concerning the underlying 2-D systems more complicated and difficult.On the other hand,with the development of networked control systems as well as the rapid advance of information technologies,the frequently occurred network-induced phenomena undoubtedly pose new challenges to the investigation of control theory.Although the study on 1-D recursive filtering issues under network environments has achieved fruitful results,the counterparts associated with the 2-D recursive filtering problems are still in the infancy.There are many important yet difficult problems to be further addressed.How to establish new methods to solve the 2-D recursive filtering problem with network-induced complexities is a significant research topic that has great application potentials yet challenging.This thesis is concerned with the recursive filtering problem of several kinds of 2-D systems with network-induced complexities.The addressed systems cover time-varying FornasiniMarchesini(F-M)models,2-D uncertain systems,2-D sensor networks,and linear repetitive processes.The network-induced complexities under consideration mainly include randomly occurring nonlinearity,package dropout,measurement degradations,randomly varying sensor delays,signal quantization,communication constraints,and stochastic filter gain disturbances.Furthermore,some novel concepts and methods are proposed to design 2-D recursive filters,such as 2-D quadratic filter,two-index time series,2-D data transmission protocol under communication constraints,2-D comparison principle,and 2-D mapping method.Attention of this thesis primarily focuses on 2-D filtering issues such as minimum-variance filtering problem,robust Kalman filtering problem,resilient filtering problem as well as distributed recursive filtering problem,thereby systematically establishing a framework of recursive filtering theory for 2-D systems.More specifically,the content of this thesis can be summarised from the following aspects:The second chapter addresses the recursive minimum-variance filtering problem for a class of 2-D time-varying systems with stochastic nonlinearity and degraded measurements.The stochastic nonlinearity is governed by its statistical characteristics and the degraded measurements reflect the signal degradation obeying certain prescribed probabilistic distributions.By constructing a two-step recursive filter and utilizing an inductive approach,unbiasedness of the proposed filter is firstly ensured and the filter parameters are then designed by resorting to the completing squares method.Subsequently,the filter performances including the boundedness and the monotonicity with respect to the measurement degradations are investigated through mathematically rigorous analysis.Moreover,a computational algorithm is presented to facilitate the online implementation of the designed filter.Finally,numerical simulation illustrates the effectiveness and applicability of the proposed filter design scheme in the state estimation problem for monitoring a long transmission line in circuit systems.The third chapter is concerned with the robust finite-horizon filter design problem for a class of 2-D discrete-time systems with norm-bounded uncertainties and incomplete measurements.The incomplete measurements cover randomly occurring sensor delays and missing measurements that are presented in a unified form by resorting to a stochastic Kronecker delta function.The main aim of this chapter is to design a recursive filter with appropriate gain parameters that ensure the local minimum of certain upper bound on the estimation error variance at each step.With the aid of the inductive approach and the 2-D Riccati-like difference equations,sufficient conditions are firstly provided for the existence of an upper bound on the estimation error variance,the matrix analysis technique is then adopted to derive such an upper bound,and finally the desired filter is designed to minimize the obtained upper bound via the gradient method.The fourth chapter investigates the resilient filtering problem for a class of 2-D systems with redundant channels and error variance constraints.In view of engineering applications,redundant channels are utilized as a protocol to schedule the message and strengthen the transmission reliability.Moreover,the implemented estimator gain is subject to stochastic perturbations satisfying specific statistical properties.By employing the induction method and the variance-constrained approach,an upper bound on the estimation error variance is firstly constructed by means of the solutions to two Riccati-like difference equations and,subsequently,a locally minimal upper bound is achieved by appropriately designing the gain parameter.Then,an effective algorithm is proposed for designing the desired estimator,which is in a recursive form suitable for online applications.A numerical simulation is also provided to demonstrate the usefulness of the proposed estimation scheme.The fifth chapter considers the finite-horizon distributed filtering problem for 2-D systems subject to stochastic communication protocol(SCP)over a sensor network.To avoid data collisions,the SCP is applied to schedule the communication between the sensor nodes and the filters through the shared channels,where only one packet received by each sensor has access to a certain channel at each transmission time.The considered scheduling behavior is characterized by mutually uncorrelated random variables with known probability distributions.Attention is paid to design the distributed filters such that the locally minimal upper bound is derived for the estimation error variance.The existence of an upper bound on the estimation error variance is first ascertained based on the intensive stochastic analysis and mathematical induction.Then,by means of a matrix simplification technique,the desired filter gains are designed to optimize the obtained upper bound at each instant.In the sixth chapter,the resilient filtering problem is investigated for a class of linear timevarying repetitive processes with communication constraints.Owing to the limited bandwidth,the communication between the sensors and the remote filter subject to uniform quantizations is carried out through a shared communication medium.To prevent data from collisions,the Round-Robin protocol scheduling is applied to orchestrate the transmission order of sensor nodes in a periodic manner,where only one sensor is permitted to obtain the network access at a certain instant so as to reduce the bandwidth usage.Moreover,stochastic perturbations on the gain parameters are taken into account in the course of the actual filter implementation.By resorting to intensive stochastic analysis and mathematical induction,sufficient condition is provided to ensure the existence of certain upper bound on the filtering error variance and acquire the gain parameters that optimize the local minimization of the derived bound.Furthermore,the boundedness issue is also discussed with respect to the filtering error variance.In addition,a numerical example is employed to demonstrate the effectiveness of the proposed filtering strategy.The seventh chapter is concerned with the recursive filtering problem for linear repetitive processes with limited network resources.Based on a two-index-depended chronological order,a new definition of the triggering-time sequence is introduced and a novel event-triggered strategy is proposed so as to reduce the communication burden as well as the energy consumption.The basic idea of event-triggered strategy is to broadcast those necessary measurements to update the innovation information only when certain events occur.As a distinct kind of2-D systems,the linear repetitive processes are firstly cast into a general F-M second model by using the lifting technique.With the aid of mathematical induction,the estimation error variance is guaranteed to have an upper bound which is then minimized with appropriate filter parameters via solving two sequences of Riccati-like difference equations.Theoretical analysis further reveals the effect of event-triggering threshold on the filtering performance.Finally,a numerical simulation is given to show the effectiveness of the designed filtering scheme.