Optimal Transport for a Class of Linear Quadratic Differential Games

Daniel Owusu Adu, Tamer Basar, Bahman Gharesifard

Research output: Contribution to journalArticlepeer-review


We consider a setting where two noncooperative players optimally influence the evolution of an initial spatial probability in a game-theoretic hierarchical fashion (Stackelberg differential game), so that at a specific final time the distribution of the state matches a given final target measure. We provide a sufficient condition for the existence and uniqueness of an optimal transport map and prove that it can be characterized as the gradient of some convex function. An important by-product of our formulation is that it provides a means to study a class of Stackelberg differential games where the initial and final states of the underlying system are uncertain, but drawn randomly from some probability measures.

Original languageEnglish (US)
Pages (from-to)6287-6294
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number11
StatePublished - Nov 1 2022


  • Convex functions
  • Costs
  • Differential games
  • Duality theory
  • Games
  • Optimal control
  • optimal transport
  • stackelberg differential game
  • Trajectory
  • Transportation
  • Stackelberg differential game

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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