Optimal Mass Transport of Nonlinear Systems under Input and Density Constraints

Abstract

We investigate optimal mass transport problem of affine-nonlinear dynamical systems with input and density constraints. Three algorithms are proposed to tackle this problem, including two Uzawa-type methods and a splitting algorithm based on the Douglas-Rachford algorithm. Some preliminary simulation results are presented to demonstrate the effectiveness of our approaches.

Figures (5)

• Figure 1: Density constraint.
• Figure 2: Density flow under constraints $|u|\le 20$
• Figure 3: Density flow under constraints $|u|\le 1$.
• Figure 4: Input on space $|u|\le 20$.
• Figure 5: Input on space, $|u|\le 1$.

Theorems & Definitions (2)

• Remark 2
• Remark 3