Séminaire hybride à l'Université McGill ou Zoom.

Optimal transport provides a powerful framework for controlling the evolution of probability distributions under dynamical systems, with applications spanning multi-agent control, generative modeling, and uncertainty propagation. This talk adopts a reverse perspective. Rather than using transport solely as a tool for distributional control, I show how it can be leveraged to reinterpret classical problems in nonlinear control through a lifted, measure-theoretic formulation. Building on existing ideas in the control literature, I present several new developments enabled by this viewpoint. In particular, transport-based characterizations yield new insights into familiar notions such as controllability and stabilizability, including linear global tests and new approaches to obstructions such as Brockett’s condition. Leveraging this framework, I also describe accompanying computational methods that naturally bridge modern generative modeling techniques in machine learning with classical control tools. Overall, the talk advocates a measure-theoretic approach to deterministic control.

Biography: Karthik Elamvazhuthi is a postdoc research associate at the Los Alamos National Laboratory. Before that he held appointments at Department of Mechanical Engineering, University of California, Riverside as a postdoctoral scholar and as a CAM (Computational and Applied Mathematics) Assistant Adjunct Professor in the Department of Mathematics, University of California, Los Angeles. He completed his Ph.D. and M.S. degrees in mechanical engineering from Arizona State University, Tempe, AZ, USA, in 2019 and 2014, respectively. His research interests lie at the intersection of control theory, robotics and machine learning. Specifically, he is interested in optimal transport of nonlinear systems, control of robotic swarms, and geometric deep learning.