Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance
This addresses density steering in control systems with unknown dynamics, but it is incremental as it builds on existing optimal transport methods.
The paper tackled the data-driven chance-constrained density steering problem for an unknown linear controlled system by using the Gromov-Wasserstein metric, and it reformulated the optimal control as a difference-of-convex program that can be efficiently solved, with numerical results validating the approach.
We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output data from pre-operational experiments are available. The initial state is modeled as a Gaussian mixture, while the terminal state is required to match a specified Gaussian distribution. We reformulate the resulting optimal control problem as a difference-of-convex program and show that it can be efficiently and tractably solved using the DC algorithm. Numerical results validate our approach through various data-driven schemes.