Optimal steering of Ensembles

We consider ensembles of particles or systems, all obeying the same dynamics or, equivalently, dynamical systems with uncertain states. In either case, we discuss i) the problem of optimally steering ensembles to a desired probability density, and ii) the problem of maintaining an ensemble at a specified admissible stationary distribution. In the context of linear dynamics and Gaussian distributions, our topic relates classical LQR and LQG theory and covariance control, while more generally it pertains to the controllability and optimal control of the Fokker-Planck and Liouville equations.