Research Collection Doctoral Thesis Stochastic motion planning for diffusions & fault detection and isolation for large scale nonlinear systems Author(s): Mohajerin Esfahani, Peyman Publication Date: 2014-01 Permanent Link: https://doi.org/10.3929/ethz-a-010163304 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library Dissertation ETH Zurich No. 21725 Stochastic Motion Planning for Diffusions & Fault Detection and Isolation for Large Scale Nonlinear Systems A dissertation submitted to ETH Zurich for the degree of Doctor of Sciences presented by Peyman Mohajerin Esfahani M.Sc., Sharif University of Technology, Tehran born 21.03.1982 in Tehran citizen of Iran accepted on the recommendation of Prof. Dr. John Lygeros, examiner Prof. Dr. Halil Mete Soner, co-examiner Prof. Dr. Karl Henrik Johansson, co-examiner January, 2014 c January 2014 Peyman Mohajerin Esfahani All Rights Reserved ISBN 978-3-906031-58-3 To my parents, Farahnaz and Hasan ... and to my wife, Farzaneh Acknowledgment When I started to write this part, I was going back and forth through countless great memories during all these years in my PhD at the Automatic Control Lab. This was indeed a unique opportunity to see many experts and leaders of different areas, and being privileged to work closely with some of them. First and foremost, I would like to express my deepest gratitude to my advisor and men- tor, Professor John Lygeros, for giving me such a wonderful opportunity and continuously supporting me with his vast knowledge and patience. This thesis only reflects part of what I have learned from him. His enthusiasm in research, sharp thinking, open-mindedness to new territories, and vision are always inspiring to me. John, it was a great pleasure and an honor to work with you; thank you for everything. Had I another chance to redo my PhD, I would definitely come back to you, and hopefully you would accept me again! It was an incredible luck for me to meet Professor Mete Soner at ETH. I would like to sincerely thank Mete not only for serving in my PhD exam committee, but also for several wonderful courses that I have taken with him during my studies. I greatly appreciate his kind willingness and precious time to share his immense knowledge and experience with me, starting from the beginning when I was just a newbie to finally as my co-examiner. I am especially grateful to Professor Karl Johansson who kindly accepted to be in my exam committee and provided me detailed and valuable comments on this thesis. Kalle, thank you also for your kind hospitality during my short visit to KTH. I owe a special thanks to Professor G¨oranAndersson. Our joint internal meetings with him during the VIKING project were always fun, yet instructive occasions. With G¨oranI had a fantastic chance to learn more about power systems. I was always amazed by his intuition in power systems, in particular when he could guess our numerical results obtained from sophisticated reachability PDEs! Thanks to Professor Manfred Morari and John, the Automatic Control Lab provided a priceless collaborative environment to work with brightest minds and genuinely friendly people. Let me start with Professor Debasish Chatterjee, to whom I am always indebted. His vast mathematical knowledge was an encouraging motivation to me, and I learned a lot from him during my first three years of PhD when he was a post-doc in our lab. Debasish, thank you so much for guiding me through these years, and of course, I will never forget that scary hand jumping out from the window late one evening at the coffee room! My special thanks go to Professor Federico Ramponi, who was not only a wonderful office- mate, but also a great teacher. His diverse and deep understanding of different topics from topology and algebra in math to programming and literature were influential to me. Sir Fed- erico, I owe you a large debt for showing me a new perspective to research, and your sentence will always stick in my mind: \never be ashamed of going back to basics". I would like also to thank Peter Hokayem for his ever kind attention and helpful discussions on scientific as well as social topics during my PhD. Peter, many thanks also for your nice hospitality at ABB; I really appreciate it. At this point, I would like to express my deep respect to my senior colleagues Andreas Milias and Stefan Richter. Andreas and Stefan, your genuinely deep knowledge and humility were always inspiring to me. You may not know of it, but you both were really influential to my view on research. I would like to thank my fantastic officemate Robin Vujanic with whom hardly do I remember a day without a fight in that office! Without Robin and Stefan I would probably never dare to step in optimization territories. Robin, I owe you also a debt of gratitude for being an ear for my nonsensical daily complaints. My special thanks also go to our chef Robert Nguyen not only for having great lunchtimes and hints on cooking (and, of course, the delicious chess cake at my defense apero!), but also for his unprecedented unbiased opinion on any topic; that was indeed instructive for me. In these years there have been many people that I have worked with and would like to offer my sincere thanks: Maria Vrakopoulou and Kostas Margellos for the collaboration in the VIKING project, Majid Zamani and Farhad Farokhi my ex-colleagues from Sharif and current collaborators, Maryam Kamgarpour, Angelos Georghiou with special thanks for listening to my last minute PhD defense rehearsal, Frauke Oldewurtel, Georg Schildbach for sharing great times discussing both technical and social topics, Tony Wood not only for being a creative collaborator but also as a good friend and fellow traveler, and Tobias Sutter with whom I have been enjoying a lot to work and learn (also many thanks for translating the thesis abstract in German). At a personal level, I want to thank my terrific Iranian friends who made my Zurich life memorable: Samira, Mahmoud, Hanieh, Farhad, Elham, and Maysam, you are simply amazing people not only for fun times, but also for always being patient and helpful to share difficult moments. Special thanks go to Mahmoud for the most relieving sentence right after the defense! I also would like to thank Arya, Kyumars, Nemat, Tofigh, Araz, Sahar, Pegah, and many others that I may have forgotten to name here. Finally, my honest and deepest thanks go to my parents, Farahnaz and Hasan, who have been supporting me through all these steps with their unconditional love and sacrifice. At this time, I want to take this opportunity to sincerely thank my brother, Payam (barat!), whose presence beside our family has always brought me invaluable confidence to continue my career far away from them. Last, but most importantly, I want to express my gratitude to my beloved wife, Farzaneh, who stood by me and patiently embraced all my tough times during these years. It would be impossible to express my feeling in words, so let me keep it simple: I love you. Peyman Mohajerin Esfahani Zurich, March 2014 ii Abstract The main theme of this thesis is twofold. First, we study a class of specifications, mainly the reachability type questions, in the context of controlled diffusion processes. The second part of the thesis is centered around the fault detection and isolation (FDI) problem for large scale nonlinear dynamical systems. Reachability is a fundamental concept in the study of dynamical systems, and in view of applications of this concept ranging from engineering, manufacturing, biology, and economics, to name but a few, has been studied extensively in the control theory literature. One particular problem that has turned out to be of fundamental importance in engineering is the so-called \reach-avoid" problem. In the deterministic setting this problem consists of determining the set of initial conditions for which one can find at least one control strategy to steer the system to a target set while avoiding certain obstacles. The focus of the first part in this thesis is on the stochastic counterpart of this problem with an extension to more sophisticated maneuvers which we call the \motion planning" problem. From the technical standpoint, this part can be viewed as a theoretical bridge between the desired class of specifications and the existing numerical tools (e.g., partial differential equation (PDE) solvers) that can be used for verification and control synthesis purposes. The second part of the thesis focuses on the FDI problem for large scale nonlinear systems. FDI comprises two stages: residual generation and decision making; the former is the subject addressed here. The thesis presents a novel perspective along with a scalable methodology to design an FDI filter for high dimensional nonlinear systems. Previous approaches on FDI problems are either confined to linear systems, or they are only applicable to low dimensional dynamics with specific structures. In contrast, we propose an optimization-based approach to robustify a linear residual generator given some statistical information about the disturbance signatures, shifting attention from the system dynamics to the disturbance inputs. The pro- posed scheme provides an alarm threshold whose performance is quantified in a probabilistic fashion. From the technical standpoint, the proposed FDI methodology is effectively a relaxation from a robust formulation to probabilistic constraints. In this light, the alarm threshold ob- tained via the optimization program has a probabilistic performance index. Intuitively speak- ing, one would expect to improve the false alarm rate by increasing the filter threshold.