LQG Control withMinimal Information: Semidefinite Programming Approach
Real-time decision-making procedures in general require continuous acquisition of information from the environment. In this talk, we revisit one of the most fundamental questions in real-time decision-making theory: what is the minimal information acquisition rate to achieve sequential decision-making with desired accuracy? We tackle this question using basic tools from control theory, information theory, and convex optimization theory.
Specifically, we consider a Linear-Quadratic-Gaussian (LQG) control problem where Massey’s directed information from the state sequence to the control sequence is taken into account. We show that the most "informationfrugal" decision-making policy achieving desired LQG control performance admits an attractive three-stage separation structure comprised of (1) an additive whiteGaussian noise (AWGN) channel, (2) Kalman filter, and (3) a certainty equivalence controller. We also show that an optimal policy can be synthesized using a numerically efficient algorithm based on semidefinite programming (SDP).
Takashi Tanaka received his B.S. degree from Tokyo University in 2006, M.S. and Ph.D. degrees from University of Illinois at Urbana-Champaign in 2009 and 2012, all in Aerospace Engineering. Currently, he is a postdoctoral associate at the Laboratory for Information and Decision Systems (LIDS) at Massachusetts Institute of Technology. His research interests are in the joint area of control, optimization, game theory and information theory.