ECE Seminar (EE290) Gradient Flows for Prediction and Control of Densities

Speaker Name: 
Abhishek Halder
Speaker Title: 
Assistant Professor
Speaker Organization: 
Department of Applied Mathematics at the University of California, Santa Cruz
Start Time: 
Monday, May 20, 2019 - 10:40am
End Time: 
Monday, May 20, 2019 - 11:40am
Location: 
E2-192
Organizer: 
Yu Zhang

Abstract: 

This talk will outline an emerging systems-theoretic viewpoint that equations for uncertainty propagation and filtering can be seen as gradient flows on the manifold of probability density functions. On one hand, this novel geometric viewpoint reveals the metric structure of these equations. On the other hand, it opens up the possibility to solve the propagation and filtering  problems without function approximation or discretization of the state space, leading to remarkably fast non-parametric computation. We will show that the same framework can be utilized for feedback control of state ensemble for nonlinear systems, where the ensemble may correspond to a population density (e.g., swarm of robots, population of neurons) or may correspond to a probability density (e.g., belief state in robot motion planning). We will provide numerical results to illustrate the ideas.
 

Bio:

Abhishek Halder is an Assistant Professor in the Department of Applied Mathematics at the University of California, Santa Cruz. Before that, he held postdoctoral positions in the Department of Mechanical and Aerospace Engineering at University of California, Irvine, and in the Department of Electrical and Computer Engineering at Texas A&M University. He obtained his BS and MS degrees from the Indian Institute of Technology in Kharagpur in 2008, and his Ph.D. from Texas A&M University in 2014, all in Aerospace Engineering. His research interests are in stochastic systems, control and optimization with application focus on large scale cyber-physical systems.