Synchronization of Nonlinear Drive and Response Systems through Robust-adaptive Feedback Control Techniques Muhammad Siddique 2018 Department of Electrical Engineering Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad, Pakistan i Thesis Examinars Name: Muhammad Siddique Department: Electrical Engineering Registration:02-7-1-030-2013 Date of Registration: 9 April 2013 Foreign Reviewers (Names and Affiliations) 1. Prof. Shen Yin, Harbin Institute of Technology, China. 2. Prof. Tariq Samad, Technological Leadership Institute USA. 3. Dr. Liangrui Peng, Tsinghua University, China. Thesis Defense Examiners (Names and Affiliations) 1. Prof. Dr. Nisar Ahmad, GIK Institute of Engineering Science and Technology. 2. Prof. Dr. Shafqat Karim, Physics Division, PINSTECH, Islamabad. 3. Prof. Dr. Imtiaz Ahmad Taj, Capital University Islamabad. Head of Department(Name): Dr. Muhammad Arif Signatures/Date: ii Thesis Submission Approval This is to certify that the work contained in this thesis entitled Synchronization of Nonlinear Drive and Response Systems through Robust-adaptive Feedback Control Techniques, was carried out by Muhammad Siddique, and in my opinion, it is fully adequate, in scope and quality, for the degree of Ph.D. Supervisor: Name: Dr. Muhammad Rehan Date: July 19, 2018 Place: PIEAS, Islamabad. Head, Department of Electrical Engineering: Name: Dr. Muhammad Arif Date: July 19, 2018 Place: PIEAS, Islamabad. iii Synchronization of Nonlinear Drive and Response Systems through Robust-adaptive Feedback Control Techniques Muhammad Siddique Submitted in partial fulfillment of the requirements for the degree of Ph.D. July, 2018 Department of Electrical Engineering Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad, Pakistan Dedications To my parents ii Acknowledgements All glory to Almighty Allah, the creator of this universe, The Gracious and the compassionate whose bounteous blessings gave me the potential thoughts, talented teachers, helping friends, loving parents, sisters and brothers and an opportunity to make this humble contribution and all the respect and Darood-O-Salam are due to His Holy Prophet Muhammad (P.B.U.H.) whose immaculate teachings flourished my thoughts and thrived my ambition all along the way to have the cherished fruit of modest effort in form of this write-up. I express my most sincere gratitude, hearty sentiments and thanks to my project supervisor Dr. Muhammad Rehan for his exlcellent supervision, encour- agement, knowledge delivery and guidance. His sweet behavior, keen interest, personal involvement and criticism for the betterment were all the real sources of courage, inspiration and strength during the completion of this thesis. I would express appreciation to my class fellows at the university especially Muhammad Awais, Najam Saqib, Muntazir Hussain and Sohaira for their contin- uous support in learning the tough conceptions. I also express my appreciation to the senior colleagues including the faculty of Electrical Engineering Department and management at NFC, IET Multan for their continuous support. Finally, I would like to express my deepest gratitude to my mother, father, brother, sisters and all other friends and relatives, for their emotional and moral support throughout my academic career and also for their love, patience, encour- agement and prayers. (Muhammad Siddique) PIEAS, Islamabad iii Declaration of Originality I hereby declare that the work contained in this thesis and the intellectual content of this thesis are the product of my own work. This thesis has not been previously published in any form nor does it contain any verbatim of the published resources which could be treated as infringement of the international copyright law. I also declare that I do understand the terms `copyright' and `plagiarism', and that in case of any copyright violation or plagiarism found in this work, I will be held fully responsible of the consequences of any such violation. (Muhammad Siddique) Date: July 19, 2018 PIEAS, Islamabad iv Copyrights Statement The entire contents of this thesis titled Synchronization of Nonlinear Drive and Response Systems through Robust-adaptive Feedback Control Techniques by Mr. Muhammad Siddique, are an intellectual property of Pakistan Institute of Engineering & Applied Sciences (PIEAS). No portion of the thesis should be reproduced without obtaining explicit permission from PIEAS. v Contents Dedications ii Acknowledgements iii Declaration of Originality iv Copyrights Statement v Contents vi Abstract xvii List of Publications and Patents xviii List of Abbreviations and Symbols xx 1 Introduction 1 1.1 Introduction . .1 1.2 Motivations . .3 1.2.1 High Power LASERS Applications . .3 1.2.2 Secure Information Transmission . .4 1.2.3 Multiple Power Generators Synchronization . .4 1.2.4 Synchronization of Two Gyros . .5 1.2.5 Synchronization of Electro-Mechanical Systems . .6 1.2.6 Application in Master and Slave clocks . .6 vi 1.2.7 Synchronization of Robots, Ships, Submarines and Aircrafts7 1.2.8 Synchronization of Biological Oscillations . .7 1.3 Control Techniques . .8 1.3.1 Observer Based Control . 10 1.3.2 Sliding Mode Control . 10 1.3.3 Synchronization by Huygen's Coupling . 11 1.3.4 Synchronizing Control by Back Stepping Techniques . 11 1.3.5 Synchronization Using Adaptive Control . 12 1.3.6 Robust Synchronizing Control . 13 1.3.7 Robust-adaptive Control for Synchronization . 14 1.4 Literature Survey . 14 1.5 Contribution of Dissertation . 18 1.6 Structure of the Dissertation . 21 2 Preludes of the Available Data 23 2.1 Nonlinear Dynamical Systems . 23 2.2 Chaos and Chaotic Systems . 25 2.3 Time-delay Systems . 28 2.4 Nonlinear Drive and Response systems . 29 2.4.1 Application of Drive and Response Systems in Real World . 30 2.4.2 Nonlinear Drive and Response Systems with Bounded Time Delay . 31 2.4.3 Nonlinear Drive and Response Systems with Uncertain De- lay Rate . 32 2.5 Error Dynamics . 33 2.6 Synchronization of Drive and Response Systems . 34 2.6.1 Types of synchronization . 35 vii 2.7 Lipschitz Nonlinearities . 36 2.8 Lyapunov Theory for Stability and Control . 37 2.8.1 Types of stability . 39 2.8.2 Lyapunov function and adaptation laws . 40 2.9 Robust Control . 42 2.10 Robust-adaptive Control . 43 2.11 Cone Complementary Linearization Algorithm . 44 2.12 Simulation Software . 45 2.12.1 MATLAB as a Simulation Software . 47 3 Adaptive Feedback Synchronizing Control for Nonlinear Drive and Response Systems 48 3.1 Introduction . 48 3.2 Statement of Systems and The Problem Formulation . 50 3.3 Synchronization Control . 53 3.4 Case1: Synchronization with Known Parameters . 54 3.4.1 Observer Based Feedback Control . 55 3.4.2 Coupled Chaotic Synchronous Observers . 56 3.4.3 Synchronization Error Dynamics for Known Parameters . 58 3.4.4 Feedback Control for Synchronization . 63 3.4.5 Simulations and Results . 72 3.5 Case2: Synchronization of Nonlinear Systems with Unknown Pa- rameters . 81 3.5.1 Coupled Chaotic Adaptive Synchronous Observers . 84 3.5.2 Synchronization Error Dynamics for Unknown Parameters . 86 3.5.3 Feedback Control for Adaptive Synchronization . 88 3.5.4 Amended Lyapunov Function . 89 viii 3.5.5 Simulation and Results . 91 3.6 Conclusion . 99 4 Robust-adaptive feedback synchronizing control for nonlinear drive and response systems 100 4.1 Introduction . 100 4.2 Problem Formulation for the Robust-Adaptive Feedback Synchro- nizing Control . 102 4.3 Coupled Chaotic Adaptive Synchronous Observers . 104 4.4 CCS Observer Based Control Methodology for Synchronization . 105 4.5 Sigma Modification for Robustness . 107 4.6 Filtering Techniques for Noise Rejection . 108 4.7 Robust-Adaptive Feedback Control . 108 4.8 Simulation and Results . 112 4.9 Conclusion . 120 5 Convex Routines for Solution of Matrix Inequalities 121 5.1 Introduction . 121 5.2 Problem Statement for The Solution of NMIs using Convex Routines123 5.3 Problem Statement for Alternate Method for The Solution of NMIs Using Convex Routines . 126 5.4 Simulation and Results . 131 5.5 Conclusion . 137 6 Delay-range-dependent adaptive control for time-delay chaotic systems 139 6.1 Introduction . 139 6.2 Generalized Model of The Delay Incorporated Systems . 142 ix 6.3 Synchronizing Error Dynamics for The Delayed Drive and The Re- sponse Systems . 145 6.4 Adaptive Synchronizing Controller Design for Delayed Containing Drive and Response Systems . 146 6.5 A Controller Design Condition for Finding the Controller Gain Ma- trix . 152 6.6 Simulation and Results . 158 6.7 Conclusion . 163 7 Robust-Adaptive Synchronization of Drive and Response Sys- tems with Varying Time Delays 165 7.1 Introduction . 165 7.2 Statement of the Generalized Model of the Nonlinear Drive and Response Systems . 167 7.3 Synchronizing Error Dynamics for the Delay Comprising Drive and The Response Systems . 169 7.3.1 Problem Formulation . 170 7.4 Synchronizing Control for Drive-Response Architecture with Un- known Parameters and Varying State Delays . 170 7.4.1 Robust-adaptive feedback control for synchronization . 171 7.4.2 Adaptation Law . 171 7.4.3 Performance index for robust control . 171 7.5 Simulation and Results . 178 7.6 Conclusion . 182 8 Summary and Future Work Directions 183 8.1 Summary . 183 x 8.2 Future Work Directions . 186 Appendix A 189 Appendix B 194 References 204 xi List of Figures 1.1 Secure information transmission by synchronization of chaotic systems4 1.2 Generic architecture of feedback control scheme . .9 2.1 The pendulum system . 24 2.2 Synchronization scheme of drive and response systems with time delay . 32 2.3 Robust-adaptive control scheme general architecture . 44 3.1 Observer based control scheme block diagram . 56 3.2 Coupling architecture for the observer based non-adaptive control scheme . 57 3.3 Phase portraits of the master and the slave FHN systems : (a) phase portrait of the master system, (b) phase portrait of the slave system. 74 3.4 Time evolutions of the normalized membrane potentials . 74 3.5 Time evolutions of the recovery variables .