Optimal Transport for a Class of Linear Quadratic Differential Games

• 成果类型: Article
• 署名作者: Adu, Daniel Owusu; Basar, Tamer; Gharesifard, Bahman
• 署名单位: Queens University - Canada; University of Illinois System; University of Illinois Urbana-Champaign; University of California System; University of California Los Angeles
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3183031
• 发表日期: 2022
• 页码: 6287-6294
• 关键词: Differential games; transportation; COSTS; games; trajectory; Convex functions; optimal control; duality theory; Optimal Transport; Stackelberg differential game

摘要

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.