Control and Estimation Methods over Communication Networks

Control and Estimation Methodsover Communication Networks

Magdi S. Mahmoud

Control and EstimationMethods overCommunication Networks

2123

Magdi S. MahmoudDepartment of Systems EngineeringKing Fahad University of Petroleum and MineralsDhahranSaudi Arabia

ISBN 978-3-319-04152-0 ISBN 978-3-319-04153-7 (eBook)DOI 10.1007/978-3-319-04153-7Springer Cham Heidelberg New York Dordrecht London

Library of Congress Control Number: 2014930316

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In the Name of

the All-Compassionate, the All-Merciful.“And of knowledge, you (mankind) have beengiven only a little.”

DedicatedTo The Memory of My ParentsTo My Family: Salwa, Medhat, Monda,Mohamed, MennaTo My Grandchildren: Malak, Mostafa,Mohamed

MsMDhahran-Saudi Arabia, 2013

Preface

From a technological viewpoint, networked control systems (NCSs) are comprisedof the system to be controlled and of actuators, sensors, and controllers whose op-eration is coordinated through some form of communication network. The widelyaccepted feature of NCSs is that the component elements are spatially distributedand may operate in an asynchronous manner, but have their operation coordinatedto achieve some overall objective. In this regard, the proliferation of these systemshas raised fundamentally new questions in communications, information process-ing, and control, dealing with the relationship between operations of the networkand the quality of the overall system operation. A wide range of recent researchactivities have been dealing with problems related to controlling the formation of adhoc networks of spatially distributed systems, system-dependent data rate require-ments in digital feedback channels, real-time fusion and registration of data fromdistributed heterogeneous sensors, and the theory of cooperative control of networksof autonomous agents.

To shed light on the evolution of control technology, one can trace the timelineof the technological evolution from classical feedback control to digital control tonetworked control. The early work dealt in an increasingly rigorous way with designprinciples of specific feedback systems. A solid theoretical foundation for frequencydomain methods was subsequently laid by many pioneering scientists. By the mid1950s, there was growing interest in the use of digital computers as instrumentationfor feedback control. In passing from the continuous-time/continuous-state modelsused in classical feedback designs to the discrete-time/quantized-state design ofdigital control, design choices involving sampling rates, effects of finite word length,and compensation for phase lags needed to be made. After half a century of researchand implementation experience, the foundations of digital control theory are nowfirmly established and can be found in textbooks.

Control systems with spatially distributed components have existed for severaldecades. Examples include chemical processes, refineries, power plants, and air-planes. In the past, in such systems, the components were connected by hardwiredconnections, and the systems were designed to bring all the information from the

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sensors to a central location where the conditions were being monitored and deci-sions were taken on how to act. The control policies then were implemented via theactuators, which could be valves, motors, etc.

What is different today is that technology can put low-cost processing powerat remote locations via microprocessors, and that information can be transmittedreliably via shared digital networks or even wireless connections. These technology-driven changes are fueled by the high costs of wiring and the difficulty in introducingadditional components into the systems as the needs change. In 1983, Bosch GmbHbegan a feasibility study of using networked devices to control different functionsin passenger cars. This appears to be one of the earliest efforts along the lines ofmodern networked control. The study bore fruit, and in February 1986, the innovativecommunications protocol of the Control Area Network (CAN) was announced at theCongress of the Society of Automotive Engineers, Detroit, MI. By mid-1987, CANhardware in the form of Intel’s 82526 chip had been introduced, and today, virtuallyall cars manufactured in Europe include embedded systems integrated through CAN.NCSs are found in abundance in many technologies, and all levels of industrialsystems are now being integrated through various types of data networks.

Throughout this book, the following terminologies, conventions, and notationshave been adopted. All of them are quite standard in the scientific media and onlyvary in form or character. Matrices, if their dimensions are not explicitly stated, areassumed to be compatible for algebraic operations. In symmetric block matrices orcomplex matrix expressions, we use the symbol • to represent a term that is inducedby symmetry.

Acknowledgments

The book is mainly targeted at senior undergraduate or graduate-level students, atacademic and industrial researchers working in the field, and also at engineers de-veloping actual solutions for control systems deploying communication networks.One can view this book as a good basis to teach a class on NCSs.

The idea of writing this book arose and developed during fall 2005, and has beenrevived after joining King Fahd University of Petroleum and Minerals (KFUPM),where I greatly took full advantage from the supportive scientific environment. Itis a great pleasure to acknowledge the financial funding afforded by Deanship ofScientific Research (DSR) through project no. IN131002 and for providing overallsupport for research activities at KFUPM.

During the last 5 years, I had the privilege of teaching various graduate courses atKFUPM, Saudi Arabia. The course notes, updated and organized, were instrumentalin generating different chapters of this book, and valuable comments and/or sug-gestions by graduate students were greatly helpful, particularly those who attendedthe courses SCE 507, SCE 527, SCE 593, and SCE 612 offered at the SystemsEngineering Department over the period 2007–2013.

A prominent place and heartfelt thanks are owed to my colleagues from all overthe world who have helped me in grasping the fundamental concepts of this excitingfield and in writing this book. Moreover, I deeply appreciate the effort of MuhammadSabih, Mirza H. Baig, Azhar M. Memon, and Gulam D. Khan for their unfailinghelp in preparing portions of the manuscript and performing effective numeroussimulations.

In writing this volume, I took the approach of referring within the text to papersand/or books which I believe taught me some concepts, ideas, and methods. I furthercomplemented this by adding some remarks, observations, and notes within andat the end of each chapter to shed some light on other related results. I apologizein advance in case I committed injustice and assure all of the colleagues that anymistake was definitely unintentional. Anonymous reviewers provided me with manyuseful comments. The help of editors and the support team at Springer, in particularOliver Jackson, was very valuable. I also want to express my deep gratitude to all theresearchers in the field who have made their results and publications easily available

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over the World Wide Web. Without this help, collecting the material discussed in thepresent book alone would have been too big a challenge.

Most of all, however, I would like to express my deepest gratitude to my parentswho taught me the value of the written word and to all the members of my family,especially my wife Salwa, for her elegant style and for proofreading parts of themanuscript. Without their constant love, incredible amount of patience, and (mostly)enthusiastic support, this volume would not have been finished.

I would appreciate any comments, questions, criticisms, or corrections thatreaders may take the trouble of communicating to me at

November 2013 Magdi S. MahmoudDhahran, Saudi Arabia

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Evolution of Control Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Data Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.2 Wireless Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.1.3 Quality of Service (QoS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.1.4 The Power Control Problem (PCP) . . . . . . . . . . . . . . . . . . . . 71.1.5 The Medium Access Control Problem (MACP) . . . . . . . . . 71.1.6 Transport Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.1.7 Asynchronous Transfer Mode (ATM) Networks . . . . . . . . . 8

1.2 Networked Control Systems (NCS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2.1 Advantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.2 Limitations and Drawbacks . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.3 Limited Communication Bandwidth . . . . . . . . . . . . . . . . . . 131.2.4 Transmission Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3 Outline of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.2 Chapter Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Role of Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Initial Design Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.1 Network Induced Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.2 NCS Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.3 Maximum Allowable Delay Bound . . . . . . . . . . . . . . . . . . . 26

2.3 Problems in Networks and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.4 Classes of Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.1 Class I Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.4.2 Class II Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.6 Suggested Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

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3 Nonstationary Packet Dropouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1.1 Models Incorporating only Packet Losses . . . . . . . . . . . . . . 413.1.2 Models Incorporating only Network Delays . . . . . . . . . . . . 433.1.3 Models Incorporating Multiple Network Phenomena . . . . . 47

3.2 Nonstationary Packet Dropouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.2.1 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.2 Stability Analysis and Controller Synthesis . . . . . . . . . . . . . 563.2.3 Uninterruptible Power System . . . . . . . . . . . . . . . . . . . . . . . 633.2.4 Autonomous Underwater Vehicle . . . . . . . . . . . . . . . . . . . . . 65

3.3 Quantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.3.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.3.2 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.3.3 Simulation Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.4 Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 843.4.1 A Class of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.4.2 Design Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.4.3 Simulation Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.5 Output-Feedback with Probabilistic Delays . . . . . . . . . . . . . . . . . . . . . 1023.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023.5.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033.5.3 Feedback Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.5.4 Simulation Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116


4 Control Over Lossy Communication Channel . . . . . . . . . . . . . . . . . . . . . . 1274.1 Output Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1284.1.2 Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1294.1.3 Simulation Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1344.1.4 Simulation Example 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

4.2 Markov Jump Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1404.2.1 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1404.2.2 Model Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1434.2.3 Completely Known Transition Matrices . . . . . . . . . . . . . . . 1474.2.4 Multiple-Packet Transmissions . . . . . . . . . . . . . . . . . . . . . . . 1534.2.5 Partially Known Transition Matrices . . . . . . . . . . . . . . . . . . 1554.2.6 Simulation Example 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

4.3 Networked Predictive Control System . . . . . . . . . . . . . . . . . . . . . . . . . 1644.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1664.3.2 System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1684.3.3 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1754.3.4 Simulation Example 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

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4.4 Dynamic Output Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1914.4.1 Model and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1934.4.2 Completely Known Transition Probability Matrices . . . . . 1974.4.3 Partially Known Transition Probability Matrices . . . . . . . . 2004.4.4 Simulation Example 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

4.5 Robust Mixed H2/H∞ Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2084.5.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2094.5.2 Stochastic Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2134.5.3 Robust H2 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2154.5.4 Robust Mixed H2/H∞ Control . . . . . . . . . . . . . . . . . . . . . . . 2164.5.5 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2184.5.6 Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221


5 Systems Under Communication Constraints . . . . . . . . . . . . . . . . . . . . . . . . 2295.1 Observer-Based Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

5.1.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2305.1.2 Closed-Loop System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2335.1.3 Feedback Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2345.1.4 Simulation Example 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2445.1.5 Simulation Example 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

5.2 LQG Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2465.2.1 Linear Quadratic over Lossy Networks . . . . . . . . . . . . . . . . 2505.2.2 Transmission Control Protocol . . . . . . . . . . . . . . . . . . . . . . . 2525.2.3 User Datagram Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2605.2.4 Estimator Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2605.2.5 Simulation Example 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2645.2.6 Simulation Example 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

5.3 Quantized H∞ Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2725.3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2745.3.2 Hold Input (HI) Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2775.3.3 Zero-Input (ZI) Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2835.3.4 Simulation Example 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2885.3.5 Simulation Example 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2905.3.6 Simulation Example 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293


6 Estimation via Network Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3036.1 State Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303

6.1.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3046.1.2 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305

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6.1.3 Estimator Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3086.1.4 Simulation Example 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

6.2 Robust Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3106.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3126.2.2 Problem Statement and Definitions . . . . . . . . . . . . . . . . . . . 3136.2.3 Robust Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3156.2.4 Simulation Example 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

6.3 H2 State Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3216.3.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3226.3.2 Stability and Performance Analysis . . . . . . . . . . . . . . . . . . . 3256.3.3 Estimator Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3286.3.4 Simulation Example 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3286.3.5 Simulation Example 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329


7 Event-Based Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3377.1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

7.1.1 Simple Demonstration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3397.1.2 Generic Model of Event-Based Loops . . . . . . . . . . . . . . . . . 3397.1.3 Network Communication Protocols . . . . . . . . . . . . . . . . . . . 3417.1.4 Event Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

7.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3427.3 Output Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

7.3.1 Event-Driven Controller Design . . . . . . . . . . . . . . . . . . . . . . 3507.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

7.4.1 Simulation Example 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3537.4.2 Simulation Example 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354

7.5 Event-Based H∞ Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3607.5.1 System Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3627.5.2 H∞ Filtering Performance Analysis . . . . . . . . . . . . . . . . . . . 3677.5.3 H∞ Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3707.5.4 Robust H∞ Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3727.5.5 Simulation Example 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373


8 Stochastic Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3858.1 H∞ Control Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

8.1.1 Model Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3868.1.2 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3888.1.3 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3998.1.4 Simulation Example 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402

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8.1.5 Simulation Example 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4048.1.6 Simulation Example 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

8.2 A Sampled-Data Network-Based Control . . . . . . . . . . . . . . . . . . . . . . . 4088.2.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4108.2.2 H∞ Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 4138.2.3 H∞ Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4198.2.4 Simulation Example 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

8.3 Observer-Based Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4238.3.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4248.3.2 Analytic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4278.3.3 Simulation Example 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433


9 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4439.1 Distributed Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

9.1.1 Controller Area Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4439.1.2 Switched Ethernet Network . . . . . . . . . . . . . . . . . . . . . . . . . . 4449.1.3 Network Effects on Control Systems . . . . . . . . . . . . . . . . . . 4459.1.4 TrueTime Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4459.1.5 Network Simulation Under Ideal Assumptions . . . . . . . . . . 4469.1.6 Information Lost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4479.1.7 Shared Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

9.2 Wireless Control of Cart with Inverted Pendulum . . . . . . . . . . . . . . . . 4499.2.1 Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4509.2.2 Network Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4539.2.3 Maximum Allowable Sampling Rate . . . . . . . . . . . . . . . . . . 4539.2.4 Effect of Channel Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4549.2.5 Sample Rate Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4579.2.6 Relevant Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4609.2.7 A Wireless Sensor Network Protocol . . . . . . . . . . . . . . . . . . 4619.2.8 A Wireless Process Control System . . . . . . . . . . . . . . . . . . . 462

9.3 Wireless Servo Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4649.3.1 Triple Inverted Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . 4669.3.2 Network Control Architecture . . . . . . . . . . . . . . . . . . . . . . . . 4699.3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471

9.4 A Networked Servo Motor System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4719.4.1 Predictive Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 4739.4.2 Experimental Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4749.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476

9.5 Wireless Area Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4819.5.1 Network Architecture, Protocol and Scheduling . . . . . . . . . 4819.5.2 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

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9.5.3 Impact of NCS on Interconnected Systems . . . . . . . . . . . . . 4849.5.4 Power System Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485


10 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49310.1 Stability Notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

10.1.1 Practical Stabilizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49310.1.2 Razumikhin Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494

10.2 Delay Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49510.3 Lyapunov Stability Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496

10.3.1 Lyapunov–Razumikhin Theorem . . . . . . . . . . . . . . . . . . . . . 49610.3.2 Lyapunov–Krasovskii Theorem . . . . . . . . . . . . . . . . . . . . . . 49810.3.3 Some Lyapunov–Krasovskii Functionals . . . . . . . . . . . . . . . 499

10.4 Probability Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50110.4.1 Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50210.4.2 The Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 503

10.5 Basic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50510.5.1 Inequality 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50510.5.2 Inequality 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50510.5.3 Inequality 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50610.5.4 Inequality 4 (Schur Complements) . . . . . . . . . . . . . . . . . . . . 50710.5.5 Inequality 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50810.5.6 Inequality 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50910.5.7 Bounding Lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

10.6 Linear Matrix Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51210.6.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51310.6.2 Some Standard Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51410.6.3 The S-Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515

10.7 Some Formulas on Matrix Inverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51610.7.1 Inverse of Block Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 51610.7.2 Matrix Inversion Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519

Notations and Symbols

I+ The set of positive integers� The set of real numbers�+ The set of nonnegative real numbers�n The set of all n-dimensional real vectors�n×m The set of n × m-dimensional real matricesC− The open right-half complex planeC+ The closed right-half complex plane∈ Belonging to or element of⊂ Subset of∪ Union∩ Intersection>> Much greater than<< Much less thanAt The transpose of matrix AA−1 The inverse of matrix AI An identity matrix of arbitrary orderIs The identity matrix of dimension s × sej The jth column of matrix Ixt or At The transpose of vector x or matrix Aλ(A) An eigenvalue of matrix Aρ(A) The spectral radius of matrix Aλj (A) The jth eigenvalue of matrix Aλm(A) The minimum eigenvalue of matrix A where λ(A) are realλM (A) The maximum eigenvalue of matrix A where λ(A) are realA−1 The inverse of matrix AA† The Moore–Penrose inverse of matrix AP> 0 Matrix P is real symmetric and positive-definiteP≥ 0 Matrix P is real symmetric and positive semi-definiteP< 0 Matrix P is real symmetric and negative-definiteP≤ 0 Matrix P is real symmetric and negative semi-definiteA(i, j ),Aij The i jth element of matrix Adet(A) The determinant of matrix A

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xviii Notations and Symbols

trace(A) The trace of matrix Arank(A) The rank of matrix AL2(−∞,∞) Space of time domain square-integrable functionsL2[0,∞) Subspace of L2(−∞,∞) with functions zero for t < 0L2(−∞, 0] Subspace of L2(−∞,∞) with functions zero for t > 0L2(j�) Square-integrable functions on C0, including at∞H2 Subspace of L2(j�) with functions Analytic in Re(s)> 0L∞(j�) Subspace of functions bounded On Re(s)= 0, including at∞H∞ The set of L∞(j�) functions analytic in Re(s)> 0|a| The absolute value of scalar a||x|| The Euclidean norm of vector x||A|| The induced Euclidean norm of matrix A||x||p The �p norm of vector x||A||p The induced �p norm of matrix AIm(A) The image of operator/matrix AKer(A) The kernel of operator/matrix Amax D The maximum element of set Dmin D The minimum element of set Dsup D The smallest number that is larger than or equal to each element

of set Dinf D The largest number that is smaller than or equal to each element

of set Darg max D The index of maximum element of ordered set Sarg min D The index of minimum element of ordered set SBr The ball centered at the origin with radius rRr The sphere centered at the origin with radius rN The fixed index set {1,2, .,N}[a, b) The real number set {t ∈ � : a ≤ t < b}[a, b] The real number set {t ∈ � : a ≤ t ≤ b}S The set of modes {1,2, ., s}iff If and only if⊗ The Kronecker productO(.) Order of (.)diag(...)A Diagonal matrix with given diagonal elementsspec(A) The set of eigenvalues of matrix A (spectrum)min − poly(A)(s) The minimal polynomial of matrix A

List of Acronyms

ARE Algebraic Riccati equationDC Decentralized controlHC Hierarchical controlLMI Linear matrix inequalitySISO Single-input single-outputMIMO Multi-input multi-outputOLD Overlapping decompositionOLC Overlapping controlTDS Time-delay systemTDUS Time-delay uncertain systemLKF Lyapunov–Krasovskii functionalDFC Decentralized feedback controlDHC Decentralized H∞ controlSVD Singular value decompositionDNS Decentralized nonlinear systemsLBD Lyapunov-based designDTS Discrete-time systemsLQC Linear quadratic controlLMCR Liquid metal-cooled reactorDSMP Decentralized servomechanism problemDIP Distributed information processingCIP Centralized information processingSMC Sliding mode control

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About the Author

Magdi S. Mahmoud has been a professor of systemsengineering since 1984. He is now a distinguished uni-versity Professor at KFUPM, Saudi Arabia. He workedat different universities worldwide in Egypt, Kuwait, theUAE, the UK, the USA, Singapore, Saudi Arabia, andAustralia. He has given invited lectures in Venezuela,Germany, China, the UK, and the USA. He has beenactively engaged in teaching and research in the devel-opment of modern methodologies to distributed control,switched time-delay systems, fault-tolerant systems, and

information technology. He is the principal author of 30 books, including bookchapters and the author/coauthor of more than 500 peer-reviewed papers. He is therecipient of two national, one regional, and four university prizes for outstandingresearch in engineering. He is a fellow of the IEE, a senior member of the IEEE,the CEI (UK), and a registered consultant engineer of information engineering andsystems (Egypt).

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Control and Estimation Methods over Communication Networks

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