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Optimal sensor and actuator placement is an important unsolved problem in control theory. Nearly every downstream control decision is affected by these sensor and actuator locations, but determining optimal locations amounts to an intractable brute-force search among the combinatorial possibilities. Indeed, there are (np) = n!/((n-p)!p!) possible choices of p point sensors out of an n-dimensional state x. Determining optimal sensor and actuator placement in general, even for linear feedback control, is an open challenge. Instead, sensor and actuator locations are routinely chosen according to heuristics and intuition. For moderate-sized search spaces, the sensor placement problem has well-known model-based solutions using optimal experiment design [1], [2], and information theoretic and Bayesian criteria [3]-[7]. As discussed in "Summary," this article explores how to design optimal sensor locations for signal reconstruction in a framework that scales to arbitrarily large problems, leveraging modern techniques in machine learning and sparse sampling. Reducing the number of sensors through principled selection may be critically enabling when sensors are costly, and it may also enable faster state estimation for low-latency, high-bandwidth control.

Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns