Control of Ensembles of Single-Input Continuous-Time Linear Systems

In this paper we consider continuous-time linear time-invariant single-input systems that depend on a single parameter. Given a family of desired states we aim to find open-loop control inputs which are independent of the parameter that simultaneously steer the zero initial state arbitrarily close to a family of terminal states. As an application we show that a family of networks of harmonic oscillators can be robustly controlled by a single input function. Thus our goal is to effectively compute open-loop input functions that are cabable of controlling an ensemble of linear systems.