Professor Daizhan Cheng
Institute of Systems Science, Academy of Mathemetics and Systems Science
Chinese Academy of Sciences
No. 55 Zhongguancun East Road, Beijing 100190, P.R. China
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic Systems
Abstract: Motivated by the semi-tensor product of matrices, which is now called the M-product, a systematic dimension-free matrix theory is proposed. It consists of M-product, V-product of matrices; M-addition, V-addition of matrices/vectors; and M-equivalence, V-equivalence of matrices/vectors. All these operators with newly developed properties form the dimension-free matrix theory. Under this new framework, all the matrices with arbitrary dimensions form a vector space M, and all the vectors with arbitrary dimensions also form a vector space V. Certain further geometric structures are explored. For instance, the fiber bundle structure of M and V over equivalence classes is obtained.
Because both M and V are dimension-free, the action of M on V becomes a cross-dimensional linear system. The trajectory of the system is calculated and certain properties are revealed. The system is naturally developed to (discrete/continuous) cross-dimensional control systems. Finally, the cross-dimensional nonlinear (control) systems are also investigated. Cross-dimensional system theory may be used to investigate dimension-varying systems such as internets, genetic networks; uncertain-dimensional systems such as superstring in theoretical physics; or engineering systems such as power generators.
Biography: Dr. Daizhan Cheng graduated from Tsinghua University in 1970, received M.S. from Graduate School, Chinese Academy of Sciences in 1981, and Ph.D. from Washington University, St. Louis, in 1985. Since 1990, he is a professor with Institute of Systems Science, AMSS, Chinese Academy of Sciences. His research interests include nonlinear control systems, switched systems, Hamiltonian systems, Boolean control networks, and game theory. He is the author/coauthor of 14 Books, over 250 Journal Papers and over 150 Conference Papers. He was Chairman of Technical Committee on Control Theory, Chinese Association of Automation (2003-2010), member of IEEE CSS Board of Governors (2009, 2015), and IFAC Council Member (2011-2014). He is IEEE Fellow (2006-), IFAC Fellow (2008-). He received Second National Natural Science Award twice (in 2008 and 1014), Outstanding Science and Technology Achievement Price of CAS (2015), and the Automatica Best Methodology/Theory Paper Award (2008-2010), bestowed by IFAC.
Professor Warren Dixon
Department of Mechanical and Aerospace Engineering
University of Florida
Room 334, MAE-B, Gainesville, FL 32611
Closed-loop Control of Man and Machine: Insights from Nonlinear, Adaptive and Switched System Methods
Abstract: Application of an electric field across skeletal muscle causes muscle contractions that produce limb movement. Clinicians have long prescribed electrical stimulation as a means to strengthen muscle; however, there is growing interest in electrical stimulation to evoke coordinated limb motions for functional tasks such as cycling. Motivation for such a cybernetic system includes advanced rehabilitative outcomes (i.e., neuroplasticity and restoration of function) for individuals with neurological disorders. A challenge to developing these outcomes is that muscle activation dynamics are uncertain and nonlinear, and the dynamics of limb motion also require the coordinated switching among multiple muscle groups. Moreover, artificial stimulation of the muscle is highly inefficient, leading to rapid muscle fatigue, which can limit the therapeutic outcomes. This talk focuses on how perspectives from and advances in robotics / robotics / control systems can be used to overcome these challenges. Underlying theories and experimental results for various closed-loop electrical stimulation methods will be described including recent advances in cybernetic cycling where a robotic bicycle is combined with an electrically stimulated person to facilitate various rehabilitative objectives.
Biography: Warren Dixon received his Ph.D. in 2000 from the Department of Electrical and Computer Engineering from Clemson University. He was selected as a Eugene P. Wigner Fellow at Oak Ridge National Laboratory (ORNL). In 2004, he joined the University of Florida in the Mechanical and Aerospace Engineering Department. His main research interest has been the development and application of Lyapunov-based control techniques for uncertain nonlinear systems. He has published 4 books, an edited collection, over a dozen chapters, and approximately 150 journal and 250 conference papers. His work has been recognized by a number of awards, most notably the 2015 & 2009 American Automatic Control Council (AACC) O. Hugo Schuck (Best Paper) Award, the 2013 Fred Ellersick Award for Best Overall MILCOM Paper, the 2011 American Society of Mechanical Engineers (ASME) Dynamics Systems and Control Division Outstanding Young Investigator Award, the 2006 IEEE Robotics and Automation Society (RAS) Early Academic Career Award, an NSF CAREER Award (2006-2011), and the 2001 ORNL Early Career Award for Engineering Achievement. He is an ASME Fellow and IEEE Fellow, an IEEE Control Systems Society (CSS) Distinguished Lecturer, and served as the Director of Operations for the Executive Committee of the IEEE CSS Board of Governors (2012-2015). For his service to the U.S. Air Force Science Advisory Board ((2012-2016), he was awarded the Air Force Commander's Public Service Award.
Professor Zhong-Ping Jiang
Department of Electrical and Computer Engineering
New York University
5 MetroTech Center, Brooklyn, NY, 11201
Network Stability and Control: A Small-Gain Paradigm
Abstract: In this talk, I will provide a historical survey of the small-gain theory for stability and control of interconnected systems. Recent developments in cyclic-small-gain theorems will be reviewed and applied to answer the first fundamental question: When is a dynamical network comprised of more than two subsystems stable? Constructive methods for the generation of Lyapunov functions for dynamical networks will be discussed. Tools such as gain assignment technique will be presented to address the second fundamental question: When can a dynamical network be made stable by feedback? In the end, the talk will end up with applications of small-gain techniques to various classical problems in robust nonlinear control design and to modern control design issues arising from quantized and event-based control of nonlinear systems. Finally, if time permits, I will present our recent work in integrating small-gain theory and adaptive dynamic programming for data-driven adaptive optimal control design.
Biography: Zhong-Ping JIANG received the B.Sc. degree in mathematics from the University of Wuhan, Wuhan, China, in 1988, the M.Sc. degree in statistics from the University of Paris XI, France, in 1989, and the Ph.D. degree in automatic control and mathematics from the Ecole des Mines de Paris, France, in 1993.
Dr. Jiang has been a Professor of Electrical and Computer Engineering at New York University. His main research interests include stability theory, robust/adaptive/distributed nonlinear control, adaptive dynamic programming and their applications to information, mechanical and biological systems. He is coauthor of the books Stability and Stabilization of Nonlinear Systems (with Dr. I. Karafyllis, Springer, 2011), Nonlinear Control of Dynamic Networks (with Drs. T. Liu and D.J. Hill, Taylor & Francis, 2014), Robust Adaptive Dynamic Programming (with Yu Jiang, IEEE-Wiley, 2017), and Nonlinear Control Under Information Constraints (with T. Liu, Science Press, 2018).
Dr. Jiang is a Senior Editor of IEEE Control Systems Letters, a Deputy co-Editor-in-Chief of the Journal of Control and Decision, an Editor for the International Journal of Robust and Nonlinear Control and has served as an Associate Editor or a Guest Editor for several journals including Mathematics of Control, Signals and Systems (MCSS), Systems & Control Letters, IEEE Transactions on Automatic Control, European Journal of Control, and Science China: Information Sciences. Dr. Jiang is a recipient of the prestigious Queen Elizabeth II Fellowship Award from the Australian Research Council, the CAREER Award from the U.S. National Science Foundation, and the Distinguished Overseas Chinese Scholar Award from the NSF of China.
Prof. Jiang is a Fellow of the IEEE and a Fellow of the IFAC.