Xudong Chen is an Assistant Professor in the Department of Electrical, Computer, and Energy Engineering at the University of Colorado Boulder. Prior to that, he was a postdoctoral fellow in the Coordinated Science Laboratory at the University of Illinois, Urbana-Champaign. He obtained the B.S. degree in Electronics Engineering from Tsinghua University, China, in 2009, and the Ph.D. degree in Electrical Engineering from Harvard University, Massachusetts, in 2014. He is an awardee of the 2020 Air Force Young Investigator Program, a recipient of the 2021 NSF CAREER award, and the recipient of the 2021 Donald P. Eckman award. His current research interests are in the area of control theory, stochastic processes, optimization, game theory and their applications in modeling, analysis, control, and estimation of large-scale complex systems.
Structure Theory for Nonholonomic Ensemble Systems
Ensemble control deals with the problem of using a common control input to simultaneously steer a large population (in the limit, a continuum) of individual control systems. In this talk, we address a fundamental problem in ensemble control theory, namely, system controllability. A key factor in determining controllability of an ensemble system is its underlying parameterization space. Roughly speaking, the bigger the parameterization space is, the more difficult one can control the ensemble. Over the past two decades, significant progress has been made for understanding controllability of ensemble systems over one-dimensional parameterization spaces, yet little is known when the dimensions are greater than one. A major focus of this talk is to present recent advances in controllability of ensemble systems whose parameterization spaces are multi-dimensional. We will consider two classes of ensemble systems, namely, ensembles of linear control systems and ensembles of control-affine systems. We will first show that linear ensemble systems are problematic if their parameterization spaces are greater than one and, then, show how to resolve this controllability issue by using a special class of control-affine ensembles whose control vector fields are equipped with a fine structure.