Control synthesis for large collections of dynamical systems with counting constraints

Abstract: Can we control a swarm of systems and give guarantees on their collective behavior? In this talk I will discuss an instance of this problem: given a large almost homogeneous collection of dynamical systems and a novel class of safety constraints, called counting constraints, how to synthesize a controller that guarantees the satisfaction of these constraints. Counting constraints impose restrictions on the number of systems that are in a particular mode or in a given region of the state-space over time. I will present an approach for synthesizing correct-by-construction controllers to enforce such constraints. Our approach exploits the structure of the problem, the permutation invariance of dynamics due to homogeneity and the permutation invariance of counting constraints, to achieve massive scalability. I will discuss several potential applications of this approach and illustrate it on the problem of coordinating a large collection of thermostatically controlled loads while ensuring a bound on the number of loads that are extracting power from the electricity grid at any given time and on a multi-robot search and rescue task.

Bio: Necmiye Ozay received the B.S. degree from Bogazici University, Istanbul in 2004, the M.S. degree from the Pennsylvania State University, University Park in 2006 and the Ph.D. degree from Northeastern University, Boston in 2010, all in electrical engineering. She was a postdoctoral scholar at the California Institute of Technology, Pasadena between 2010 and 2013. She joined the University of Michigan, Ann Arbor in 2013, where she is currently an associate professor of Electrical Engineering and Computer Science and a core faculty at Michigan Robotics Institute. Dr. Ozay’s research interests include hybrid dynamical systems, control, optimization and formal methods with applications in cyber-physical systems, system identification, verification & validation, autonomy and dynamic data analysis. Her papers received several awards including a Nonlinear analysis: Hybrid Systems Prize Paper Award for years 2014-2016. She has received five young investigator awards, including NSF CAREER, and the 1938E Award and a Henry Russel Award from the University of Michigan for her contributions to teaching and research.