CSL student wins IEEE CDC Best Paper Award
At the flagship conference for control theory this past December in France, several CSL faculty and students watched proudly as Jin-Won Kim won the Best Student Paper Award for his research, “What is the Lagrangian for Nonlinear Filtering.”
“This award is a tremendous honor, not only for Jin-Won Kim, but also for the MechSE Department and the Coordinated Science Laboratory,” said Prashant Mehta, CSL associate professor and Kim’s advisor.
Kim’s paper, written with Mehta and former CSL Professor Sean Meyn (now at the University of Florida), is on the mathematical topic of duality between optimal control and optimal estimation.
The classical result on this problem appears in the celebrated 1961 paper of Kalman and Bucy. In this seminal paper, the Kalman-Bucy filter was first derived. It was also shown that the problem of optimal (minimum variance) estimation is dual to a certain optimal control problem.
Sixty years have elapsed since the original Kalman-Bucy paper. Although long recognized to be an important topic, it was a widely-held belief that the duality expressed in that paper, is a linear artifact that does not generalize to nonlinear settings. Mehta suggested the problem to Kim, as he had done with many other students, in the hope that studying this question could lead to better approximation algorithms for the estimation problem.
“I have wrestled with this generalization for the past ten years,” Mehta said. “I did not really expect him to solve the problem.”
Kim’s formulation is an exact generalization, in the sense that the dual optimal control problem has the same minimum variance structure for linear and nonlinear estimation problems. Kalman-Bucy’s classical result is shown to be a special case.
While the current work is “purely theoretical,” Kim believes it is a good start. The paper opens up new mathematical tools to conduct analysis of estimation algorithms and suggests new ways to construct approximations that had not previously been considered. The potential of his work likely contributed to Kim receiving this recognition.
“This award is a great honor, and while some may say it’s enough to think about the theory, I am seeking more applications,” said Kim. “This is the starting point and the award is encouraging me to work more on this topic.”
This research was supported by grants from the Army Research Office and the National Science Foundation.