ABSTRACT: Directed information is an information-theoretic measure that can be interpreted as a directional information flow between random processes. The concept has been broadly used in causality analysis, as well as in the analysis of communication systems with feedback. In this talk, we discuss the fundamental trade-off between the best achievable control performance and the required feedback directed information. We first discuss several engineering and scientific applications (e.g., networked control systems design, optimal perception design, non-equilibrium thermodynamics) in which such a trade-off study plays fundamental roles. We then introduce some mathematical preliminaries and numerical solution algorithms, including (i) the semidefinite programming approach for linear-quadratic-Gaussian systems, and (ii) the forward-backward Arimoto-Blahut iteration for finite state systems.

BIOSKETCH: Takashi Tanaka is an Assistant Professor in the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin. He received his B.S. degree from the University of Tokyo in 2006, M.S. and Ph.D. degrees from UIUC in 2009 and 2012, all in Aerospace Engineering. Prior to joining UT Austin, he held postdoctoral researcher positions at MIT and KTH Royal Institute of Technology. His research interests include control, optimization, game theory, information theory, and their applications to distributed decision-making problems.