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Duality-based Dynamical Optimal Transport of Discrete Time Systems

Wu, Dongjun LU and Rantzer, Anders LU orcid (2025) In IEEE Transactions on Automatic Control
Abstract

We study dynamical optimal transport of discrete time systems (dDOT) 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. Additionally, the proposed algorithm is highly amenable to parallelization. For linear systems with Gaussian... (More)

We study dynamical optimal transport of discrete time systems (dDOT) 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. Additionally, the proposed algorithm is highly amenable to parallelization. For linear systems with Gaussian marginals, we provide a semi-definite programming formulation based on our theory. Finally, we validate the approach with a simulation example.

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Please use this url to cite or link to this publication:
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publication status
epub
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in
IEEE Transactions on Automatic Control
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:105016863459
ISSN
0018-9286
DOI
10.1109/TAC.2025.3611060
language
English
LU publication?
yes
additional info
Publisher Copyright: © 1963-2012 IEEE.
id
1b52d143-db3e-4687-b374-a9504f12a44c
date added to LUP
2025-12-09 10:21:09
date last changed
2025-12-19 14:20:07
@article{1b52d143-db3e-4687-b374-a9504f12a44c,
  abstract     = {{<p>We study dynamical optimal transport of discrete time systems (dDOT) 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. Additionally, the proposed algorithm is highly amenable to parallelization. For linear systems with Gaussian marginals, we provide a semi-definite programming formulation based on our theory. Finally, we validate the approach with a simulation example.</p>}},
  author       = {{Wu, Dongjun and Rantzer, Anders}},
  issn         = {{0018-9286}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Transactions on Automatic Control}},
  title        = {{Duality-based Dynamical Optimal Transport of Discrete Time Systems}},
  url          = {{http://dx.doi.org/10.1109/TAC.2025.3611060}},
  doi          = {{10.1109/TAC.2025.3611060}},
  year         = {{2025}},
}