Dynamic Analysis For Networked Two-Dimensional Systems Under Different Communication Protocols

The filtering/control problems of two-dimensional(2-D)systems have been one of the hot topics in the field of control theories.The theory of 2-D systems originates from the study of multi-dimensional linear filtering.The most significant difference between the 2-D systems and the one-dimensional(1-D)ones is that the former evolves along two different directions(usually called the horizontal direction and vertical direction),which have been extensively utilized in the fields of image processing,water heating,seismic data analysis and processing etc.In recent years,with the rapid development of communication/computer technologies,networked 2-D systems have attracted much attention from many scholars in various fields.In the networked 2-D systems,each part of the system is connected to a shared network,and the data is transmitted through the network.In the process of data transmission,the shared network is usually configured with corresponding communication protocols to avoid the occurrence of data congestion.Usually,the communication protocols are classified into the static scheduling protocols(such as the Round-Robin protocol),the stochastic communication protocols(such as the ALOHA protocol and the Carrier Sense Multiple Access protocol),and the dynamic scheduling protocols(such as the Try-Once-Discard protocol).At present,most of the research concerning control theories based on communication protocols mainly focuses on the 1-D systems,and the corresponding analysis/synthesis for 2-D systems have not been fully carried out,and some key problems still need to be further explored.This thesis aims to discuss the filtering and control problems of networked 2-D systems under the influence of different communication protocols,such as the H_?state estimation problem under the Round-Robin(R-R)protocol,the dissipative filtering problem under the redundant channel protocol,the H_?filtering problem under the stochastic communication protocol(SCP),and the feedback control problem under the random access protocol(RAP).The network-induced phenomena in this study mainly include:randomly occurring uncertain-ty,signal quantization,randomly occurring nonlinearity(RON),sensor delay,channel noise and non-fragile filter gains.In order to deal with the above mentioned problems,the stochas-tic analysis method,the matrix inequality technique,the 2-D parameters design method as well as the Lyapunov stability theory are adopted.In the introduction,part,i.e.,Chapter1,we introduce in detail the application backgrounds of the 2-D systems,the main commu-nication protocols with their different working principles in 2-D systems,the recent research achievements of networked 2-D systems under various communication protocols as well as their deficiencies,which result in the problems to be solved in the current research.According to different problems concerned the main content of this thesis is organized from the following five parts.In Chapter 2,the robust H_?state estimation problem is addressed for the 2-D discrete systems under logarithmic quantization and R-R protocol.The norm-bounded uncertainties are also involved in the considered system,which are governed by two stochastic variables satisfying the Bernoulli distribution.In this chapter,we introduce the signal transmission model under the R-R protocol.The purpose of this chapter is to design a state estimator to make the proposed estimation error system meet the predefined performance indicator.Through in-depth stochastic analysis,sufficient conditions for the robust stability of the 2-D augmented error system are given,and the results are further extended to achieve the robust H_?stability for the augmented error system.Explicit expressions of the estimator gains are also given by solving certain matrix inequalities.Effectiveness of the proposed estimation method is verified by an numerical example.In Chapter 3,the non-fragile dissipative filtering problem is investigated for the 2-D sys-tems subjected to randomly occurring uncertainties and redundant channel protocol.For the redundant channel transmission,if a signal fails to be transmitted through a certain channel,the next channel is immediately activated to transmit the signal once again.The norm-bounded uncertainties are introduced in the considered system,which are governed by two stochastic variables obeying the Bernoulli distribution law.The aim of this chapter is to design a dis-sipative filter in a non-fragile manner such that the augmented filtering error system is not only asymptotically stable in the mean-square sense but also satisfies a strict 2-D(Q,S,R)-?-dissipativity performance index.Based on the Lyapunov theory and stochastic analysis,sufficient conditions are first given to guarantee the asymptotic stability of the 2-D system in the mean-square sense.Then,the non-fragile filter is designed to ensure that the 2-D system satisfies the strict 2-D(Q,S,R)-?-dissipativity performance index,under which the expres-sions of the non-fragile filter gains are given by solving certain matrix inequalities.Finally,a simulation example is provided to show the effectiveness of the proposed dissipative filtering method.In Chapter 4,the robust H_?filtering problem is investigated is concerned for the 2-D system in Roesser model with RON and SCP.The introduced nonlinearity is sector-like and governed by a random variable obeying the Bernoulli distribution law.The SCP is depicted by an independent and identically distributed sequence to schedule the signal transmission.The phenomenon of time delay is also taken into consideration.The aim of this chapter is to design a filter such that the augmented filtering error system satisfies a predefined H_?performance index.Sufficient condition is first given to ensure the robust stability of the augmented filtering error system via Lyapunov theory and stochastic analysis.Then,the result is extended to guarantee the H_?performance of the augmented system with RON under SCP,where sufficient criterion related to the transmission probability is given in terms of matrix inequality.Moreover,the filter gains are explicitly designed which enable the system to achieve the H_?filtering performance.Finally,a numerical example is given to show the effectiveness of the proposed design method.In Chapter 5,the H_?control problem is investigated for a time-delayed 2-D network under the RAP.The control input is transmitted to the actuator via a network with communication constraint,and the RAP is adopted here to schedule the data transmission which is depicted by an independent and identically distributed sequence.The aim of the addressed problem is to design an observer-based controller so that the considered 2-D system has a predefined H_?performance index.Sufficient condition is given to ensure the H_?performance of the closed-loop system via the Lyapunov theory and stochastic analysis.Moreover,the observer-based controller is dexterously designed to ensure the achievement of the H_?performance,under which the controller gains are designed by solving certain matrix inequalities.Finally,a numerical example is given to demonstrate effectiveness of the proposed approach.In Chapter 6,the observer-based output feedback H_?control problem is investigated for the 2-D networked control system(NCS)under periodic scheduling protocol and redundant channels.The controller-to-actuator(C/A)network performs a periodic scheduling protocol and the sensor-to-controller(S/C)network uses the redundant channel protocol.The C/A net-work is considered where only one controller obtains the access to the communication network at each transmission instant.The periodic scheduling protocol assigns the communication access rights to the actuator in a chronological order.The aim of the proposed problem is to design an observer-based output feedback controller so that the 2-D NCS satisfies a predefined H_?performance index.Sufficient condition is given to ensure the H_?performance of the closed-loop system via Lyapunov theory and stochastic analysis.Moreover,the observer-based output feedback controller is designed by solving some matrix inequalities which can be cast in-to certain convex optimization problems.Finally,a numerical example is given to demonstrate the effectiveness of the proposed approach.Finally,in the end of this thesis,we conclude the paper,and some future research topics are proposed.