Control and Estimation of Systems with Input Output Delays

✍ Scribed by Huanshui Zhang; Lihua Xie

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 227
• Series: Lecture Notes in Control and Information Sciences 355
• Edition: 1
• Category: Library

✦ Synopsis

Time delays exist in many engineering systems such as transportation, communication, process engineering and networked control systems. In recent years, time delay systems have attracted recurring interests from research community. Much of the effort has been focused on stability analysis and stabilization of time delay systems using the so-called Lyapunov-Krasovskii functional together with a linear matrix inequality approach, which provides an efficient numerical tool for handling systems with delays in state and/or inputs. Recently, some more interesting and fundamental development for systems with input/output (i/o) delays has been made using time domain or frequency domain approaches. These approaches lead to analytical solutions to time delay problems in terms of Riccati equations or spectral factorizations. This monograph presents simple analytical solutions to control and estimation problems for systems with multiple i/o delays via elementary tools such as projection. We propose a re-organized innovation analysis approach for delay systems and establish a duality between optimal control of systems with multiple input delays and smoothing estimation for delay free systems. These appealing new techniques are applied to solve control and estimation problems for systems with multiple i/o delays and state delays under both the H2 and H-infinity performance criteria.

✦ Table of Contents

Preface......Page 5
Symbols and Acronyms......Page 7
Contents......Page 9
1.1 Definition of Krein Spaces......Page 14
1.2 Projections in Krein Spaces......Page 16
1.3 Kalman Filtering Formulation in Krein Spaces......Page 17
1.4 Two Basic Problems of Quadratic Forms in Krein Spaces......Page 18
1.5 Conclusion......Page 19
2.2 Single Measurement Delay Case......Page 20
2.3 Multiple Measurement Delays Case......Page 30
2.4 Conclusion......Page 39
3.1 Introduction......Page 40
3.2 Linear Quadratic Regulation......Page 41
3.3 Output Feedback Control......Page 54
3.4 Examples......Page 57
3.5 Conclusion......Page 63
4.1 Introduction......Page 66
4.2 H_∞ Fixed-Lag Smoothing......Page 67
4.3 H_∞ d-Step Prediction......Page 82
4.4 H_∞ Filtering for Systems with Measurement Delay......Page 90
4.5 Conclusion......Page 98
5.1 Introduction......Page 100
5.2 H_∞ Full-Information Control Problem......Page 101
5.3 H_∞ Control for Systems with Preview and Single Input Delay......Page 119
5.4 An Example......Page 124
5.5 Conclusion......Page 126
6.1 Introduction......Page 128
6.2 Linear Minimum Mean Square Error Estimation for Measurement Delayed Systems......Page 129
6.3 H_∞ Filtering for Systems with Multiple Delayed Measurements......Page 135
6.4 H_∞ Fixed-Lag Smoothing for Continuous-Time Systems......Page 145
6.5 Conclusion......Page 154
7.1 Introduction......Page 156
7.2 Problem Statements......Page 157
7.3 H_∞ Smoothing......Page 158
7.4 H_∞ Prediction......Page 170
7.5 Conclusion......Page 175
8.1 Introduction......Page 176
8.2 Linear Quadratic Regulation......Page 177
8.3 Measurement Feedback Control......Page 191
8.4 H_∞ Full-Information Control......Page 198
8.5 Conclusion......Page 216
References......Page 218
Index......Page 224