Abstract
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 language | English (US) |
---|---|
Pages (from-to) | 6287-6294 |
Number of pages | 8 |
Journal | IEEE Transactions on Automatic Control |
Volume | 67 |
Issue number | 11 |
DOIs | |
State | Published - Nov 1 2022 |
Keywords
- 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