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Decentralized Networked Control Systems: Control and Estimation Over Lossy Channels

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Decentralized Networked Control Systems: Control and Estimation Over Lossy Channels University of Sharjah College of Engineering Department of Electrical and Computer Engineering DECENTRALIZED NETWORKED CONTROL SYSTEMS: CONTROL AND ESTIMATION OVER LOSSY CHANNELS by Muhammad Ali S. M. Al-Radhawi Supervisor Professor Maamar Bettayeb Program Master of Science in Electrical Engineering January 12, 2011 DECENTRALIZED NETWORKED CONTROL SYSTEMS: CONTROL AND ESTIMATION OVER LOSSY CHANNELS by Muhammad Ali S. M. Al-Radhawi A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Electrical and Computer Engineering, University of Sharjah Approved by: Maamar Bettayeb ..................................... Chairman Professor of Electrical Engineering, University of Sharjah Abdulla Ismail ........................................ ..............Member Professor of Electrical Engineering, United Arab Emirates University Qassim Nasir ......................................... ..............Member Associate Professor of Electrical Engineering, University of Sharjah January 12, 2011 ii (( )) "O my Lord! increase me in knowledge" (Quran XX.114) (( )) "Are they equal, those who know and those who know not?" (Quran XXXIX.9) iii Acknowledgements First and foremost, the completion of this thesis has been merely by the grace of God, and through Him I have been able to understand and appreciate the real beauty and value of mathematics, and knowledge in general. I would like to sincerely and deeply thank my advisor, Professor Maamar Bettayeb. His support, and encouragement helped me a lot through the steps of my thesis. I will always appreciate and remember the many hours that we used to spend in his office discussing various research directions. At times he had more faith in me than I, and I hope that my work lived up to some of his expectations. I thank Prof. Abdulla Ismail for taking the time to serve on my thesis committee. I also thank Dr. Qassim Nasir for serving in the committee, and for years of friendship and help. I am also thankful to the faculty members at the Department, namely, Dr. Karim Abed-Meraim, and Dr. Ahmed Elwakil for their friendship, and collaboration. I also thank friends whom I have met while pursuing my degrees, namely my officemate Mahmoud Nabag. Finally, I would like to extend my deepest gratitude and respect to my parents for their support. iv Contents Acknowledgements iv Table of Contents v List of Figures ix Abstract xii Notation and Acronyms xiv 1 Introduction and Relevant Work 1 1.1 Motivation..................................... 1 1.1.1 Motivating Applications for Decentralized Networked Control Systems 2 1.1.2 The Gap Between Decentralized and Networked Control Research . 4 1.2 NetworkedControlSystems(NCSs) . .... 4 1.2.1 NCSissues................................. 6 1.2.2 PacketDropoutModels ......................... 8 1.2.3 Overview on Stability and Controller Synthesis over Lossy Links . 10 1.3 Decentralized/Distributed Control . ........ 12 1.3.1 System Decomposition and Decentralization Structures........ 12 1.3.2 Overview on Decentralized Control Methods . ..... 14 1.4 Decentralized Networked Control Systems (DNCS) . ........ 16 1.4.1 DNCS Configurations . 16 1.4.2 PreviousStudiesonDNCS. 16 1.5 Problem Formulation and Scope of Work . 19 1.5.1 DecentralizedControlProblems . 20 1.5.2 DecentralizedEstimationProblems . 22 1.5.3 SimulationTools ............................. 23 1.6 Organization of the Thesis and Summary of Contributions .......... 23 v 1.6.1 Summary of Contributions . 23 1.6.2 Organization of the Thesis . 24 2 Control Theoretical Background 26 2.1 Introduction.................................... 26 2.2 LinearMatrixInequalities . 27 2.2.1 Linear Matrix Inequalities with Rank Constraints . ....... 29 2.3 Discrete-Time Markovian Jump Linear Systems (DMJLSs) . ....... 30 2.4 TheBoundedRealLemma............................ 31 2.4.1 A Variation on the Bounded Real Lemma . 32 2.5 H Control.................................... 34 ∞ 2.5.1 TheStateFeedbackProblem. 35 2.5.2 The Output Feedback Problem . 37 2.5.3 TheFilteringProblem .......................... 38 2.6 QuadraticStability .............................. 38 2.7 The S-Procedure ................................. 40 3 Decentralized State-Feedback Control With Packet Losses 42 3.1 Introduction.................................... 42 3.2 Decentralized State-feedback Control with Packet Losses ........... 43 3.3 Decentralized H Disturbance Attenuation . 45 ∞ 3.3.1 H ProblemFormulation . 45 ∞ 3.3.2 TheMainResult ............................. 46 3.3.3 ProofofTheorem3.1........................... 47 3.3.4 The case of Markov chain satisfying πij = πj .............. 50 3.3.5 Local-Mode Dependent Control . 51 3.4 Guaranteed Cost Decentralized Controller Design Via Linear Matrix Inequalities 53 3.4.1 Guaranteed Cost Problem Formulation . 53 3.4.2 Themainresult.............................. 55 3.4.3 ProofofTheorem3.3........................... 57 3.4.4 The case of Markov chain satisfying πij = πj .............. 60 3.4.5 Local-Mode Dependent Control . 61 3.5 ExamplesandSimulation . 63 3.5.1 Example I: Local-mode dependent H design for a DNCS . 63 ∞ 3.5.2 Example II: Local-mode dependent Guaranteed Cost design for a DNCS 68 3.6 Conclusions and Future Work . 70 vi 4 Decentralized Output-Feedback Control With Packet Losses 71 4.1 Introduction.................................... 71 4.2 Interconnected Networked Control Systems with Packet Losses........ 72 4.3 Decentralized H Output Feedback Controller Synthesis . 74 ∞ 4.3.1 H ProblemFormulation . 74 ∞ 4.3.2 Themainresult.............................. 76 4.3.3 ProofofTheorem4.1........................... 77 4.3.4 The case of Markov chain satisfying πij = πj .............. 78 4.3.5 Cone-Complementarity Linearization Algorithm . ........ 79 4.3.6 Local-Mode Dependent Control . 80 4.4 Decentralized Guaranteed Cost Output Feedback Controller Synthesis . 82 4.4.1 Guaranteed Cost Problem Formulation . 82 4.4.2 Themainresult.............................. 85 4.4.3 ProofofTheorem4.3........................... 86 4.4.4 The case of Markov chain satisfying πij = πj .............. 88 4.4.5 Local-Mode Dependent Control . 89 4.5 ExamplesandSimulation . 91 4.5.1 Example I: Local-mode dependent H design for a networked large- ∞ scalecontrolsystemwithpacket-losses . 91 4.5.2 Example II: Local-mode dependent Guaranteed Cost design for a net- worked large-scale control system with packet-losses . ...... 94 4.6 Conclusions and Future Work . 101 5 Decentralized H - Estimation With Packet Losses 102 ∞ 5.1 Introduction.................................... 102 5.2 Interconnected Networked Systems with Packet Losses . .......... 103 5.3 System Description and Problem Formulation . ....... 105 5.4 Decentralized H Estimator Design Via Linear Matrix Inequalities . 107 ∞ 5.4.1 ProofofTheorem5.1........................... 108 5.5 The case of Markov chain satisfying πij = πj .................. 108 5.6 Local-Mode Dependent Decentralized Estimators . ......... 109 5.7 ExampleandSimulation . 111 5.8 Conclusions and Future Work . 116 6 Application to Dynamic Routing Problem With Switching Topology and Interconnected Time-Delays 117 6.1 Introduction.................................... 117 vii 6.2 Network Modeling and Problem Formulation . 118 6.2.1 NetworkModel .............................. 118 6.2.2 PhysicalConstraints . 120 6.2.3 PerformanceObjective . 120 6.3 Decentralized H Control for DMJLS With Interconnected Time-Delays . 121 ∞ 6.3.1 ProblemFormulation. 121 6.3.2 ControllerSynthesis . 122 6.3.3 ProofofTheorem6.1........................... 122 6.4 Decentralized H Controller Applied to Dynamic Routing . 124 ∞ 6.4.1 Incorporating Physical Constraints . 124 6.4.2 Application of the decentralized controller to dynamic routing . 126 6.5 SimulationExample ............................... 127 6.6 Conclusions and Future Work . 131 7 Stability Analysis of Distributed Overlapping Estimation Scheme with Markovian Packet Dropouts 132 7.1 Introduction.................................... 132 7.2 The Decentralized Overlapping Estimator . ....... 134 7.2.1 Problem Formulation, and the Estimation Algorithm . ....... 134 7.2.2 TheEstimationErrorDynamics. 136 7.3 Necessary and Sufficient Conditions for Mean-Square Stability . 137 7.4 Sufficient Conditions for Mean Stability for Markovian and Arbitrary Losses 138 7.5 Simulation..................................... 141 7.5.1 Example1................................. 141 7.5.2 Example2................................. 141 7.6 Conclusions and Future Work . 144 8 Conclusion and Future Directions 147 8.1 Conclusions .................................... 147 8.2 FutureDirections ................................ 148 Bibliography 150 Publications by the Author 163 Abstract in Arabic 165 viii List of Figures 1.1 Some applications of DNCSs. 5 1.2 AsingleloopNCS ................................ 6 1.3 Possible positions of the network in the decentralized control system: (a) controllers communicate with the subsystems through a network, (b) The systems interact with each other through a network, (c) controllers exchange informationthroughanetwork. 16 1.4 Block diagram of the decentralized Networked Control System with distur- banceattenuation. ................................ 20 1.5 Block diagram of the decentralized filtering problem. ........... 22 1.6 Block diagram of the distributed filtering problem. .......... 23 2.1 Standard H Control Problem Block Diagram . 35 ∞ 3.1 Block diagram of the decentralized NCS with state feedback and disturbance input. ......................................
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