## Department Colloquium

### Friday, September 20th, 2019

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Xudong Chen (CU Boulder)

**Title:** Structure Theory for Ensemble Control and Estimation of Nonholonomic Systems.

**Abstract: ** Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of individual control systems. As a dual, ensemble estimation deals with the problem of using a finite number of measurement outputs to estimate the initial state of every individual system in the (continuum) ensemble. We introduce in the talk a novel class of ensembles of nonlinear control systems, termed distinguished ensemble systems. Every such system has two key components, namely a set of finely structured control vector fields and a set of co-structured observation functions. In the first half of the talk, we demonstrate that the structure of a distinguished ensemble system can significantly simplify the analysis of ensemble controllability and observability. Moreover, such a structure can be used as a principle for ensemble system design. In the second half of the talk, we address the issue about existence of a distinguished ensemble system for a given manifold. We will focus on the case where the underlying space of every individual system is an arbitrary semi-simple Lie group or its homogeneous space.

**Professor Chen** is an Assistant Professor at the University of Colorado, Boulder. Before that, he was a postdoctoral fellow in the Coordinated Science Lab at UIUC. He obtained his 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 large-scale networked systems.