Consider a distributed control problem with a communication channel connecting the observer of a linear stochastic system to the controller. The goal of the controller is minimize a quadratic cost function. The most basic special case of that cost function is the mean-square deviation of the system state from the desired state. We study the fundamental tradeoff between the communication rate r bits/sec and the limsup of the expected cost b, and show a lower bound on the rate necessary to attain b. The bound applies as long as the system noise has a probability density function. If target cost b is not too large, that bound can be closely approached by a simple lattice quantization scheme that only quantizes the innovation, that is, the difference between the controller's belief about the current state and the true state.
|Original language||English (US)|
|Title of host publication||2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)|
|Publisher||Institute of Electrical and Electronics Engineers (IEEE)|
|Number of pages||8|
|State||Published - Feb 13 2017|