2017/05/29 by Takashi Tanaka, Peyman Mohajerin Esfahani, Sanjoy K. Mitter · 1 citation
Engineering · #Stability and Control of Uncertain Systems #Advanced Control Systems Optimization #Control Systems and Identification
paper · doi:10.1109/tac.2017.2709618
openalex publication_date 2017/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We consider a discrete-time linear-quadratic-Gaussian (LQG) control problem, in which Massey's directed information from the observed output of the plant to the control input is minimized, while required control performance is attainable. This problem arises in several different contexts, including joint encoder and controller design for data-rate minimization in networked control systems. We show that the optimal control law is a linear-Gaussian randomized policy. We also identify the state-space realization of the optimal policy, which can be synthesized by an efficient algorithm based on semidefinite programming. Our structural result indicates that the filter-controller separation principle from the LQG control theory and the sensor-filter separation principle from the zero-delay rate-distortion theory for Gauss-Markov sources hold simultaneously in the considered problem. A connection to the data-rate theorem for mean-square stability by Nair and Evans is also established.