Duality-Based Dynamical Optimal Transport of Discrete Time Systems

• 成果类型: Article
• 署名作者: Wu, Dongjun; Rantzer, Anders
• 署名单位: Lund University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3611060
• 发表日期: 2026
• 关键词: OPTIMAL MASS TRANSPORTATION; Covariance control

摘要

We study dynamical optimal transport of discrete time systems with Lagrangian cost. The problem is approached by combining optimal control and Kantorovich duality theory. Based on the derived solution, a first order splitting algorithm is proposed for numerical implementation. While solving partial differential equations is often required in the continuous time case, a salient feature of our algorithm is that it avoids equation solving entirely. Furthermore, it is typical to solve a convex optimization problem at each grid point in continuous time settings, the discrete case reduces this to a straightforward maximization. In addition, the proposed algorithm is highly amenable to parallelization. For linear systems with Gaussian marginals, we provide a semidefinite programming formulation based on our theory. Finally, we validate the approach with a simulation example.