Abstract
This paper considers the optimal control of linear systems where measurement data is transmitted from the plant output to the controller over a noiseless communication channel with limited instantaneous data rate. The cost is defined to be the average, over a random initial state, of the usual infinite horizon quadratic regulation criterion, and the number of bits transported by the channel during each sampling interval is bounded. Several fundamental properties of the optimal cost functional are derived for initial state densities that satisfy a mild moment condition. Using these properties, precise expressions for the optimal cost and policy are obtained assuming a uniformly distributed initial state. These expressions agree with the classical optimal LQR results in the high data rate limit and with recent minimum rate results in the low rate regime. Extensions to the case of non-uniform densities and vector-valued states are discussed.
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