Stochastic Control Via Optimal Transport
A fundamental stochastic control problem is to steer a dynamical system between uncertain states so as to optimize suitable performance criteria. The state of the system at respective points in time is characterized by probability distributions, and the control problem is exemplified by the requirement to transition between two such distributions with minimal energy cost. Motivation for such problems stems from engineering applications that include aircraft and missile guidance, navigation, spacecraft landing, and the control of chemical and manufacturing processes, to mention a few. In such applications, a "hard'' constraint to reach a specified deterministic state is obviously unrealistic, while the common practice of affecting the end-point distribution via a terminal penalty is imprecise. Thus, motivated by the desire for precise control of state-uncertainty, we replace the aforementioned alternatives by the "soft" probabilistic constraint to specify explicitly the target distribution, and we explore ways to solve such problems in a systematic manner. The foundations of this emerging formalism can be traced to the subject of optimal mass transport theory, which provides natural metrics on probability densities that happen to be amenable to the tools of stochastic control. In this talk, I will discuss basic paradigms that help link the two fields, optimal mass transport and stochastic control, and then discuss several related ongoing projects.
Yongxin Chen received his B.S. in mechanical engineering from Shanghai Jiao Tong University, China, in 2011, and a Ph.D. degree in mechanical engineering, under the supervision of Tryphon Georgiou, from University of Minnesota in 2016. He currently serves as an assistant professor in the Daniel Guggenheim School of Aerospace Engineering at Georgia Institute of Technology. Before joining Georgia Tech, he had a one-year research fellowship at Memorial Sloan Kettering Cancer Center from August 2016 to August 2017 and was an assistant professor in the Department of Electrical and Computer Engineering at Iowa State University from August 2017 to August 2018. He has conducted researches in stochastic control, optimal transport and optimization.