On the Computation of Control Inputs for Linear Ensembles

In this paper, we revisit the classical ensemble control formulation and provide a solution to the longstanding problem of systematically designing input signals that realize a desired steering between two ensemble states. We present a new computational approach based on a suitable discretization of the integral operator related to the ensemble formulation. Specifically, we apply different methods to appropriately discretize the range operator of the ensemble system, by which we obtain a computational procedure to synthesize control signals that steer ensembles in both a robust and minimum energy fashion. We also present an extension to the previously introduced polynomial approximation technique, which is a closely related special case. This yields a unified framework for the ensemble control of linear systems, which is illustrated by means of computational examples.