Modeling and Control of Collective Dynamics

We present an overview of our recent work on the modeling and control of collective dynamics. This work provides implementable solutions to the Schroedinger bridge problem and has potential application to stochastic optimal control, optimal transport, and various generalizations. We discuss the case of degenerate constant diffusion coefficients and the steering of linear dynamical systems between two one-time state-distributions using state feedback, the limiting case of Optimal Mass transport with nontrivial prior dynamics. For the special case of Gaussian marginals, closed-form solutions will be presented. [The presentation is based on joint work with Tryphon T. Georgiou and Michele Pavon.]
Yongxin Chen was born in Ganzhou, Jiangxi, China. He received his BSc in Mechanical Engineering from Shanghai Jiao Tong university, China, in 2011. He is now a fifth-year Ph.D. student in Mechanical Engineering under the supervision of Tryphon Georgiou. Meanwhile he is pursuing a Ph.D. minor in Mathematics.

He is interested in the application of mathematics in engineering and theoretical physics. His current research focuses on linear dynamical systems, stochastic processes and optimal mass transport theory. He has worked on state covariance completion problems in connection to problems in fluid dynamics, the reversibility and manifestations of the time-direction in second-order stochastic processes, position control for pinned and Schrodinger bridges.