Measurements: Finite-Horizon Control Applications

SUMMARY In this paper, we study finite-length signal reconstruction over a finite-rate noiseless channel. We allow the class of signals to belong to a bounded ellipsoid and derive a universal lower bound on a worstcase reconstruction error. We then compute upper bounds on the error that arise from di!erent coding schemes and under di!erent causality assumptions. When the en coder and decoder are noncausal, we derive an upper bound that either achieves the universal lower bound or is comparable to it. When the decoder and encoder are both causal operators, we show that within a very broad class of causal coding schemes, memoryless coding prevails as optimal, imposing a hard limitation on reconstruction. Finally, we map our general reconstruction problem into two important control problems 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. The first problem is to minimize a finite-horizon weighted tracking error between the remote system output and a reference command. The second