Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 37-52 |
Journal | IEEE Transactions on Automatic Control |
Volume | 63 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2018 |
Bibliographical note
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.Keywords
- control over communications
- Kalman filtering
- LMIs
- stochastic optimal control
- communication networks