LQG control with minimum directed information

LQG control with minimum directed information: Semidefinite programming approach

Tanaka, T. (The University of Texas at Austin)
Mohajerin Esfahani, P. (TU Delft Team Tamas Keviczky)
Mitter, S.K. (Massachusetts Institute of Technology)

2018

We consider a discrete-time Linear-QuadraticGaussian (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 & Evans is also established.

control over communications
Kalman filtering
LMIs
stochastic optimal control
communication networks

http://resolver.tudelft.nl/uuid:d9db1c11-fbfd-4c0c-b66f-f341b49fa61a

https://doi.org/10.1109/TAC.2017.2709618

2017-11-29

0018-9286

IEEE Transactions on Automatic Control, 63 (1), 37-52

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

journal article

© 2018 T. Tanaka, P. Mohajerin Esfahani, S.K. Mitter