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LQG Control with Minimal Information: Three-Stage Separation Principle and SDP-based Solution Synthesis


T. Tanaka, P. Mohajerin Esfahani, Sanjoy Mitter

vol. AUT15-08, submitted for publication (arXiv:1510.04214)

In the interest of quantifying the minimal information for feedback control, this paper proposes a framework of linear-quadratic-Gaussian (LQG) control theory in which Massey's directed information from the state sequence to the control sequence is taken into account. Interpretation of this framework is given in the context of networked control theory. As the main result, we show that a control policy attaining required LQG control performance with minimum directed information can be realized by a three-stage decision architecture comprised of (1) a linear sensor with additive Gaussian noise, (2) a Kalman filter, and (3) a certainty equivalence controller. It is also shown that an optimal policy can be synthesized by semidefinite programming (SDP). Both time-varying finite-horizon problems and time-invariant infinite-horizon problems are considered. Our results can be viewed as a generalization of the data-rate theorem for mean-square stability by Nair & Evans, extended for a control performance analysis.


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(04)Technical Report

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% Autogenerated BibTeX entry
@TechReport { TanEsf:2015:IFA_5258,
    author={T. Tanaka and P. Mohajerin Esfahani and Sanjoy Mitter},
    title={{LQG Control with Minimal Information: Three-Stage
	  Separation Principle and SDP-based Solution Synthesis}},
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