Input-Output Data-Driven Sensor Selection

In this paper, we design a learning-based sensor selection procedure for an unknown cyber-physical system. In particular, a set of sensors that maximize a metric of observability of the system is chosen, but without using knowledge of the system’s dynamics. The metric of observability is related to the notion of the ${\mathcal{H}}_{2}$ norm, which quantifies the strength of the sensor signals generated under a given control input excitation. It is shown that the evaluation of this metric boils down to solving a set of model-based Lyapunov equations which, however, is a task that cannot be carried out directly since the system is unknown. Nevertheless, we tackle this by expressing the metric solely with respect to input-output data, and we use the new expression to choose the best sensors for the system in a model-free manner, and in polynomial time. Simulations are performed to demonstrate the efficiency of the proposed approach.