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研究生:游仁德
研究生(外文):Jen-te Yu
論文名稱:跨網路動態控制系統最佳控制之新設計
論文名稱(外文):A New Optimal Control for Networked Systems
指導教授:傅立成傅立成引用關係
指導教授(外文):Li-Chen Fu
口試委員:吳政郎林俊良陳博現張時中張帆人王文俊廖德祿高崇堯
口試委員(外文):Jeng-Lang WuChun-Liang LinBor-Sen ChenShi-Chung ChangFan-Ren ChangWen-June WangTeh-Lu LiaoChung-Yao Kao
口試日期:2015-07-27
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:電機工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:107
中文關鍵詞:跨網路最佳控制
外文關鍵詞:LQ ControlLossy NetworksMAS SynchronizationDistributed Kalman Filtering
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This dissertation aims at extending classical optimal control theories such as Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) control, and Kalman Filtering (KF) to Networked Systems (NS). There are many important and active subjects in NS research, and this dissertation focuses on two of them. The systems and network topologies under consideration are linear and time-invariant.
The first subject of this dissertation is concerned with LQ control where signal dropouts could occur. Under TCP-like protocols, the overall loop considered here is closed by lossy communication networks. Only the class of static and latest signal based compensators will be considered. We cover from simpler case of state feedback and output feedback LQR with one lossy network to more complex case of LQG control that involves two lossy networks. A new optimal control will be developed to deal with the signal dropout problem, which also links the compensator selection to the minimization of the LQ cost.
The second subject covers two synchronization problems of Multi-Agent Systems (MAS). The first problem concerns with how to achieve state synchronization for a MAS consisting of homogeneous linear time-invariant systems, given that the initial conditions for all agents are different and arbitrary and only output can be used. The second problem deals with how to reach synchronization for distributed Kalman filtering consisting of heterogeneous sensor networks and a linear mobile target that is to be traced, under the condition that the initial estimates of the target’s state are different and arbitrary for all the agents. We introduce novel notions such as relative-input-output and agent-wise coupling strength and propose a unified approach to tackle these two synchronization problems. Using the new designs proposed in this work, we will be able to eliminate all the observers used in existing designs when dealing with the first synchronization problem. For the second synchronization problem, both designs that achieve exponential synchronization and finite-time synchronization will be provided for the distributed Kalman filtering in heterogeneous sensor networks in comparison with the asymptotic synchronization presented in a popular work. Unlike many existing works, the controller and coupling strength in our new designs do not involve the full knowledge of the Laplacian matrix. Nor do they require consensus region analysis. Our agent-wise definition of coupling strength also brings in an additional benefit – its fast adaptation and high adaptability to network topology changes.
We will provide numerical examples to validate the new designs and compare their performances against that of existing works in the literature.


Contents
Acknowledgement i
Abstract ii
List of Figures vi
List of Tables viii
Chapter 1 Introduction 1
1.1 Motivation and Objectives 1
1.2 Scope 5
1.3 Contributions 6
1.4 Organization of the Dissertation 7
Chapter 2 A New LQR over a Lossy Network 9
2.1 Introduction 9
2.2 Classical State Feedback LQR 12
2.3 State Feedback LQR across a Lossy Network 13
2.4 The Optimal Compensator 16
2.5 Numerical Examples 22
Chapter 3 Output Feedback LQR over a Lossy Network 25
3.1 Introduction 25
3.2 Classical Output Feedback LQR 26
3.3 Output Feedback LQR over a Lossy Network 27
3.4 The Optimal Compensator 29
3.5 Numerical Example 34
Chapter 4 LQG Control over Two Lossy Networks 37
4.1 Introduction 37
4.2 Classical LQG Control 39
4.3 New LQG Control over Two Lossy Networks 40
4.4 The Optimal Compensator Design 45
4.5 Numerical Example 48
Chapter 5 Synchronization of Multi-Agent Systems 50
5.1 Introduction 50
5.2 A Relative-Input-Output Approach 55
5.3 Main Theorem 57
5.4 Numerical Examples 64
Chapter 6 Synchronization of Distributed Filtering in Sensor Networks 75
6.1 Introduction 75
6.2 Classical Centralized Kalman Filtering 76
6.3 Relative-State-Input Approach 78
6.4 Main Theorems 80
6.5 Numerical Examples 86
Chapter 7 Conclusions and Future Works 95
7.1 Conclusions 95
7.2 Future Works 96
References 98


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