Mean Field Type Control with Congestion
نویسندگان
چکیده
منابع مشابه
Mean field type control with congestion
We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.
متن کاملMean Field Type Control with Congestion (II): An Augmented Lagrangian Method
This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite diff...
متن کاملAn Augmented Lagrangian Method for Mean Field Type Control with Congestion
The theory of mean field type control aims at describing the behaviour of a large number of interacting agents using a common feedback. A type of problems that have recently raised a lot of interest concerns congestion effects. These problems model situations in which the cost of displacement of the agents increases in regions where the density is large (as, for instance, in crowd motion). We o...
متن کاملDynamic Programming for Mean-Field Type Control
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...
متن کاملMean Field Control Hierarchy
In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrained by a PDE of continuity-type, governing the dynamics of the probability distribution of the agent population. We show the existence of mean field optimal controls both in the stochastic and deterministic setting. We derive rigorously the first order...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics & Optimization
سال: 2016
ISSN: 0095-4616,1432-0606
DOI: 10.1007/s00245-016-9342-8