In this paper, we consider a set up in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a finite-rate noiseless channel. When control must be done over a communication channel, there is a fundamental tradeoff between allowing enough time for reconstruction of signals over the channel and achieving performance in finite-time. Most work in the area of control under communication constraints have addressed infinite-horizon control objectives (eg. stability, disturbance rejection). In this paper, we study a finite-horizon navigation problem. Our task is to navigate the state of the remote system from a nonzero initial condition, which lies in a bounded set, to as close to the origin as possible in finite-tune. We compute lower and upper bounds on the worst-case performance as a function of the channel rate, time horizon, and system parameters. We achieve the lower bound with a noncausal coding scheme and show that imposing causality on the coding scheme degrades performance. We illustrate how the bounds behave under various scenarios and show tradeoffs between time and performance accuracy.
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