'Institute of Electrical and Electronics Engineers (IEEE)'
Doi
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 (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 Schroedinger 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