Methods of Distributed and Nonlinear Process Control: Structuredness, Optimality and Intelligence A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Wentao Tang IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Advised by Prodromos Daoutidis May, 2020 c Wentao Tang 2020 ALL RIGHTS RESERVED Acknowledgement Before meeting with my advisor Prof. Prodromos Daoutidis, I was not determined to do a Ph.D. in process control or systems engineering; after working with him, I could not imagine what if I had chosen a different path. The important decision that I made in the October of 2015 turned out to be most correct, that is, to follow an advisor who has the charm to always motivate me to explore the unexploited lands, overcome the obstacles and make achievements. I cherish the freedom of choosing different problems of interest and the flexibility of time managing in our research group. Apart from the knowledge of process control, I have learned a lot from Prof. Daoutidis and will try my best to keep learning, about the skills to write, present and teach, the pursuit of knowledge and methods with both elegance of fundamental theory and a promise of practical applicability, and the pride and fervor for the undertaken works. \The high hill is to be looked up to; the great road is to be travelled on."1 I want to express my deepest gratitude to him. Prof. Qi Zhang always gives me very good suggestions and enlightenment with his abundant knowledge in optimization since he joined our department. It was a joy to consult him for fresh ideas and interchange our views on a wide variety of things. Qi is not only an intelligent researcher, a thoughtful teacher, but also a generous friend. I still owe him a countless number of meals so far. I would like to thank my great colleagues: Nahla Alamoodi, Andrew Allman, Davood Babaei Pourkargar, Pedro Constantino, Udit Gupta, Victoria Jones, Lixia Kang, Shaaz Khatib, Jingjun Liu, Abdulla Malek, Ilias Mitrai, Nitish Mittal, Manjiri Moharir, Matthew Palys, Hanchu Wang, and Michael Zachar, with whom sharing the office space and discussing the research projects have always been very pleasing. Former mem- bers Seongmin Heo, Sujit Jogwar and Srinivas Rangarajan laid important foundations for a part of my research, and the outstanding works of Michael Baldea, Panagiotis Christofides, and Aditya Kumar introduced me to the history of our group's research when I was starting my work. I have learned many skills and great ideas from my colleagues, and our collaborations turned out to be very fruitful as reflected by our coauthored papers. I am also glad that some of my ideas will continued to be developed by younger members of our group. \I am not one who was born in the possession of knowledge; I am one who is fond of antiquity, and earnest in seeking it there".2 Thanks to the teachings of all the professors 1Classic of Poetry: Minor Odes of Kingdom: Che Xia (《i經·小Å·Ê舝》). 2Analects (of Confucius): Shu Er (《論語·述而》). i that have delivered the courses in chemical engineering, control, and optimization that I have taken during the first two years before my preliminary exam, especially Professors Mihailo Jovanovi´c,Andrew Lamperski, Zhi-Quan Luo and Shuzhong Zhang, I have gained the fundamentals of these disciplines to start my research. I would not be able to list the names of all the authors of the books, chapters, papers and tutorial materials that I have read, whose works have refreshed my understanding of the relevant areas as well as my own research over and over again, and the friends in the process systems engineering and control areas that I have talked to from time to time. During the painful processes of submitting and revising papers, I have encountered some sharp but anonymous reviewers who gave very critical but constructive comments. Their opinions forced me to enhance my understanding of many relevant problems. Of course, this Ph.D. is built upon my previous 16 years of study. I feel obligated to express my gratitude to the education received from my great teachers. Ms. Zhu Qiaohua (1巧華) in Lengshuitan Fourth Elementary School taught me Mathematics and told me right from wrong during the pupil years. In Nanya Middle school, Mr. Li Weiqing (NI清) was my first formal English teacher who developed a great interest in this language. The History classes by Mr. Yin Chi'e (9³T) taught me to understand things always in combination with their history. In Yali High School, Mr. Zhang Liu's (5鎏) Mathematics was my most enjoyable course, and I became an engineering student largely due to his encouragement. Mr. Zhou Shuqiao's (h9¬) Chinese class made me a fan of ancient literature and linguistics, and Mr. Li Yun's (N贇) Philosophy left me a deep impression of his dialectic and abstract lines of thinking. At Tsinghua University, Profs. Wentao Zhu (1文濤), Diannan Lu (盧Ç`) and Lixin Yu (YË新) delivered great lectures in Physical Chemistry, Chemical Engineering Thermodynamics, and Principles of Chemical Engineering, respectively. When doing my second degree in Mathematics, the rigor of Prof. Tianquan Chen (s)權)'s Real Analysis and the elegance of Profs. Meirong Zhang (章梅®) and Huaiyu Jian's (!懷玉) Ordinary and Partial Differential Equations attracted me a lot. I learned Russian as a Secondary Foreign Language from Prof. Min Zhang (5O) for a year, which turned out to be helpful when I dive into the classical control theorists' papers. Doing a Ph.D. in this frigid and strange land is not an easy journey. The doctors and nurses at Boynton Clinics, the unknown citizens who helped me to move my car out of snows, and the chestnut chicken and grilled fish at Tea House Restaurant all made me much warmer through the long-lasting winters. The help from my friends largely ii relieved my difficulties during my first semesters in Minnesota and after my little car went missing. I am grateful to the fate that has brought my beloved wife Yixin Ye and me together. She has always been the one that cheers me up in sadness, accompanies me in difficulties, encourages me in frustrations, and shares every little mood { be it proud, delight, upset or anger { that floats in my mind from time to time. For so many times in the flight to Pittsburgh, I looked through the clouds, and saw a little rainbow above the ripples of Lake Michigan reflecting the sun's beams; I realized that she was awaiting at the destination. There might be more rivers and oceans for us to travel across, more streets and valleys for us to walk through, more gains and losses coming into our lives, but the meaning of this journey is but a journey together with her. Due to the very apparent reason, I am returning home less frequently, but my families' unwavering love can always be felt. Born in an ordinary family, I understand that it was uneasy for my parents to raise me up and find me good education faraway from home for years. Knowing that they are well has always been the biggest motivation for my hardworking, although not being able to do much for them is in turn a source of guilt. And when missing my small hometown in southwestern Hunan, I would read in my heart a poem of it:3 High upon Mount Jiuyi, white clouds diffuse; ]·q上}雲飛， Down to the green hills, by wind descended the Princesses. 帝PX¨下翠®。 They sparkled the wild bamboos with their tears so profuse, 斑ù一枝C滴淚， when the clouds turned rosy behind their layers of dresses. 紅霞,5~Íc。 Waves of Dongting surge against the overwhelming snows; 洞­波g#)ê， Folks of Long Isle chant to the rhyme of earth-shaking poems. w島ºL動0i。 And when I was lost in this broad and untrammeled dream, 我2因K"寥廓， the land of hibiscus is covered with the morning sun's gleam. 芙蓉國Ïá朝暉。 3Mao Zedong, A Rhyme of Qil¨u:Reply to a Friend (毛¤q《七律·T˺》), 1961. iii To my wife and my parents iv Abstract Chemical processes are intrinsically nonlinear and often integrated into large-scale net- works, which are difficult to control effectively. The traditional challenges faced by process control, as well as the modern vision of transitioning industries into a smart manufacturing paradigm, requires the instillation of new perspectives and application of new methods to the control of chemical processes. The goal is to realize highly automated, efficient, well-performing and flexible control strategies for nonlinear, in- terconnected and uncertain systems. Motivated by this, in this thesis, the following three important aspects (objectives) for contemporary process control { structuredness, optimality, and intelligence { are discussed in the corresponding three parts. 1. For the control of process networks in a structured and distributed manner, a network-theoretic perspective is introduced, which suggests to find a decompo- sition of the problem according to the block structures in the network. Such a perspective is examined by sparse optimal control of Laplacian network dynamics. Community detection-based methods are proposed for input{output bipartite and variable-constraint network representations and applied to a benchmark chemical process. 2. For the optimality of control, we first derive a computationally efficient algo- rithm for nonconvex constrained distributed optimization with theoretically prov- able convergence properties { ELLADA, which is applied to distributed nonlinear model predictive control of a benchmark process system. We derive bilevel op- timization formulations for the Lyapunov stability analysis of nonlinear systems, and stochastic optimization for optimally designing the Lyapunov function, which can be further integrated with the optimal process design problem.