A Lagrangian Approach for Aggregative Mean Field Games of Controls with Mixed and Final Constraints

Autor: J. Frédéric Bonnans, Justina Gianatti, Laurent Pfeiffer

Publikováno v: SIAM Journal on Control and Optimization. 61:105-134

The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the distributions

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c12289356659dd60344710c6a8790c26
https://doi.org/10.1137/21m1407720

Taylor expansions of the value function associated with a bilinear optimal control problem

Autor: Laurent Pfeiffer, Tobias Breiten, Karl Kunisch

Publikováno v: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2019, 36 (5), pp.1361-1399. ⟨10.1016/j.anihpc.2019.01.001⟩
Annales de l'Institut Henri Poincaré C, Analyse non linéaire
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2019, 36 (5), pp.1361-1399. ⟨10.1016/j.anihpc.2019.01.001⟩
Annales de lInstitut Henri Poincaré C, Analyse non linéaire

International audience; A general bilinear optimal control problem subject to an infinitedimensional state equation is considered. Polynomial approximations of the associated value function are derived around the steady state by repeated forma ldiffe

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::96677d8b6dc8c28780bf3dd0bcf085cd
https://doi.org/10.1016/j.anihpc.2019.01.001

Weak solutions for potential mean field games of controls

Autor: Alan Mullenix, P. Jameson Graber, Laurent Pfeiffer

Publikováno v: Nonlinear Differential Equations and Applications
Nonlinear Differential Equations and Applications, 2021, 28 (5), Paper No 50, 34 p. ⟨10.1007/s00030-021-00712-9⟩
Nonlinear Differential Equations and Applications, Springer Verlag, 2021, 28 (5), Paper No 50, 34 p. ⟨10.1007/s00030-021-00712-9⟩

International audience; We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a person

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd08a43d5b1dc304c6b51d45099a4c75
https://inria.hal.science/hal-03058249

Discrete-time mean field games with risk averse-agents

Autor: J. Frédéric Bonnans, Pierre Lavigne, Laurent Pfeiffer

Publikováno v: ESAIM: Control, Optimisation and Calculus of Variations
ESAIM: Control, Optimisation and Calculus of Variations, 2021, ⟨10.1051/cocv/2021044⟩
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2021

We propose and investigate a discrete-time mean field game model involving risk-averse agents. The model under study is a coupled system of dynamic programming equations with a Kolmogorov equation. The agents' risk aversion is modeled by composite ri

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::219705d37f845e237765a394d52c10c8
http://arxiv.org/abs/2005.02232

Infinite-Horizon Bilinear Optimal Control Problems: Sensitivity Analysis and Polynomial Feedback Laws

Autor: Laurent Pfeiffer, Karl Kunisch, Tobias Breiten

Publikováno v: SIAM Journal on Control and Optimization

An infinite-horizon optimal control problem subject to an infinite-dimensional state equation with state and control variables appearing in a bilinear form is investigated. A sensitivity analysis w...

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e26d2a03aead20b027d373db074e4cee
https://doi.org/10.1137/18m1173952