Value of Information in Feedback Control: Global Optimality

Abstract

The rate-regulation trade-off defined between two objective functions, one penalizing the packet rate and one the state deviation and control effort, can express the performance bound of a networked control system. However, the characterization of the set of globally optimal solutions in this trade-off for multi-dimensional controlled Gauss-Markov processes has been an open problem. In the present article, we characterize a policy profile that belongs to this set. We prove that such a policy profile consists of a symmetric threshold triggering policy, which can be expressed in terms of the value of information, and a certaintyequivalent control policy, which uses a conditional expectation with linear dynamics.

Feedback Control Over Noisy Channels: Characterization of a General Equilibrium

“…We should emphasize that the energy-regulation trade-off studied in this article can be reduced to a rate-regulation trade-off when per k is restricted to take values only in {0, 1}. In such a problem, which we have studied in [28], [29], instead of the energy the packet rate is penalized, and the scheduler's decision at each time is to transmit a message or not to transmit. Hence, our result here generalizes the result in [28], [29], where we found an optimal policy profile consisting of a symmetric threshold triggering policy and a certainty-equivalent control policy.…”