Karthik Elamvazhuthi
Los Alamos National Lab
Seminar Information
Optimal transport theory provides a general framework for controlling the evolution of probability distributions under dynamical systems, with applications spanning multi-agent control, generative modeling, and uncertainty propagation. Many applications of transport can be seen as extensions of classical control problems, to the space of probability densities. This talk adopts a reverse perspective. Rather than using transport solely as a tool for distributional control, I show how classical control problems themselves can benefit through a lifted, measure-theoretic formulation. I present several new developments enabled by this viewpoint. Transport-based characterizations yield new insights into familiar issues such as controllability and stabilizability, including linear global tests, new perspectives to address obstructions such as Brockett’s condition and performing reachability analysis. Leveraging this framework, I also describe accompanying computational methods that naturally bridge modern generative modeling techniques with classical nonlinear control tools. Overall, the talk advocates a measure-theoretic approach to nonlinear control.
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 range from developing optimal transport tools for nonlinear control systems to control of robotic swarms and geometric deep learning.