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.