Optimal Transport Over a Linear Dynamical System
Open Access Publications from the University of California

Optimal Transport Over a Linear Dynamical System

• Author(s): Chen, Yongxin
• Georgiou, Tryphon T
• Pavon, Michele
• et al.

Published Web Location

https://doi.org/10.1109/tac.2016.2602103
Abstract

We consider the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ($\dot x(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport (OMT) problem. In general, we show that the problem can again be reduced to solving an OMT problem and that it has a unique solution. In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a Schr\"odinger bridge. As the white noise intensity tends to zero, the flow of densities converges to that of the deterministic dynamics and can serve as a way to compute the solution of its deterministic counterpart. The solution can be expressed in closed-form for Gaussian initial and final state densities in both cases.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.