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Consider a flying drone controlled from the ground by an observer who communicates with it via wireless. We are interested in how well the drone can be controlled via a channel that accepts r bits/sec. Formally, the controller of a linear stochastic system aims to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We characterize the optimal tradeoff between the communication rate r bits/sec and the limsup of the expected cost b.
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