期刊
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
卷 179, 期 1, 页码 332-357出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-018-1365-7
关键词
Mean-field games; Linear stochastic systems; Weakly interacting particle system; McKean-Vlasov dynamics; Optimal control
资金
- National Science Foundation [ECCS-1509387]
- Air Force Office for Scientific Research [FA9550-15-1-0045, FA9550-17-1-0435]
- Army Office of Research [W911NF-17-1-0429]
- University of Padova Research Project [CPDA 140897]
The purpose of this work is to pose and solve the problem to guide a collection of weakly interacting dynamical systems (agents, particles, etc.) to a specified terminal distribution. This is formulated as a mean-field game problem, and is discussed in both non-cooperative games and cooperative games settings. In the non-cooperative games setting, a terminal cost is used to accomplish the task; we establish that the map between terminal costs and terminal probability distributions is onto. In the cooperative games setting, the goal is to find a common optimal control that would drive the distribution of the agents to a targeted one. We focus on the cases when the underlying dynamics is linear and the running cost is quadratic. Our approach relies on and extends the theory of optimal mass transport and its generalizations.
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