AAE Colloquium: Dr. Xudong Chen
|Event Date:||March 1, 2018|
|School or Program:||Aeronautics and Astronautics
Structure Theory for Controlling an Ensemble of Non-holonomic Systems
Dr. Xudong Chen
Electrical, Computer, & Energy Engineering
University of Colorado, Boulder
Ensemble control deals with the problem of using a few control signals to simultaneously steer a large population (or in the limit, a continuum) of control systems. These systems are structurally identical, but may show variations in tuning parameters. Ensemble control originates from physics, or more specifically, quantum mechanics. In spectroscopic applications such as NMR spectroscopy, optical spectroscopy, and magnetic resonance imaging, experiments are often performed on quantum ensembles of size on the order of 1023 rather than on individual molecules or atoms. Recently, with the rapid development of self-driving cars, unmanned aerial vehicles, robotic insects, etc., ensemble control will have a great potential impact in design and control of large-scale multi-agent autonomous systems.
In this talk, we focus on a fundamental design problem: Given a continuum ensemble of non-holonomic systems, how to co-design the control modes of each system and the tuning parameters so that the ensemble is controllable. It is well known from geometric control theory that for a single control-affine system, the work of Frobenius, Chow and Rashevsky yielded a criterion, relying on the rank of the Lie algebra generated by the control vector fields, for checking the controllability of the system. However, such a condition is far from sufficient for controlling a continuum ensemble. We introduce here an innovative method for addressing the co-design problem for ensemble controllability, which leverages structure theory of semi-simple Lie algebras developed by Elie Cartan. In a nutshell, the method simplifies the co-design problem by dividing it into two subproblems — one is about the controllability of each single system and the other is about function approximation — which can be addressed independently. Examples illustrating the key idea of the method will be given along the talk.
Xudong Chen is Assistant Professor in the Department of Electrical, Computer and Energy Engineering at the University of Colorado, Boulder. Before that, he was a postdoctoral fellow in the Coordinated Science Laboratory at the University of Illinois, Urbana-Champaign. He obtained the B.S. degree from Tsinghua University, China, in 2009, and the Ph.D. degree in Electrical Engineering from Harvard University in 2014. His research interests are in the area of control theory, stochastic processes, optimization, game theory and their applications in modeling and control of networked systems.