Model Reduction in Physical Domain

Modeling is an essential part of the analysis and the design of dynamic systems. Contemporary computer algorithms can produce very detailed models for complex systems with little time and effort. However, over complicated models may not be efficient. Therefore, reducing a model to a more manageable size has become an attractive research topic. A very useful type of reduced models is obtained by removing as many physical components as possible from the original model. Such approach is known as model reduction in the physical domain. Many results have been achieved in model reduction in the physical domain during past decades. Nonetheless, the newest developments in engineering practice as well as in theoretical research have brought about further challenges and opportunities. In this thesis, the criteria and the scope of model reduction in the physical domain are reinvestigated. As a result, a criterion based on the H,, norm of certain error model is proposed. Furthermore, the scope of model reduction is also extended. In this thesis, a mathematical framework is constructed for model reduction in physical domain. Specifically, model reduction problem is formulated as an optimization problem with bilinear matrix inequality (BMI) constraints. A branch-and-bound algorithm is developed to solve the BMI problem. The algorithm is proved to converge to global optimum. Several examples are presented to illustrate the use of the proposed model reduction scheme. Thesis Supervisor: Kamal Youcef-Toumi Title: Professor Acknowledgments I would like to thank my thesis advisor, Professor Kamal Youcef-Toumi for his advice and support. My Ph.D. program would not be the same without his knowledge, understanding and patience. I have had a very productive time with him. I am also immensely grateful to my thesis committee members, Professor Haruhiko Asada, Professor Neville Hogan and Professor Alexandre Megretski. They have made extraordinary contribution to my thesis work. Furthermore, Professor Asada has provided me precious opportunities, academically and financially, via d'Arbeloff Home Automation and Healthcare Consortium under his leadership. Also, I have benefited tremendously from working for Professor Hogan, a caring supervisor and a insightful scholar, as a teaching assistant. And the professionalism of Professor Megretski has been a major driving force behind my research effort. My thesis work is shaped with vital advice from many researchers. Among them are Professor Qingtai Ye of Shanghai Jiaotong University, Quanlin "Kate" Zhou, Isaac C. Kao and Bei Gu of MIT. Professor Masakazu Kojima and Mituhiro Fukuda of Tokyo Institute of Technology have provided me their BMI solver. In addition, I shall thank my colleagues at the Mechatronics Research Laboratory for their support. This thesis is dedicated to my parents.