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Optimal sensor and actuator selection is a central challenge inhigh-dimensional estimation and control. Nearly all subsequent controldecisions are affected by these sensor/actuator locations, and optimalplacement amounts to an intractable brute-force search among the combinatorialpossibilities. In this work, we exploit balanced model reduction and greedyoptimization to efficiently determine sensor and actuator selections thatoptimize observability and controllability. In particular, we determinelocations that optimize scalar measures of observability and controllabilityvia greedy matrix QR pivoting on the dominant modes of the direct and adjointbalancing transformations. Pivoting runtime scales linearly with the statedimension, making this method tractable for high-dimensional systems. Theresults are demonstrated on the linearized Ginzburg-Landau system, for whichour algorithm approximates known optimal placements computed using costlygradient descent methods.

Optimal Sensor and Actuator Selection using Balanced Model Reduction