A Quadratic Mean Field Games Model for the Langevin Equation

Camilli, Fabio

doi:10.3390/axioms10020068

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…In [3] a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation, and the cost is quadratic, was addressed. An appropriate change of variables transforms the Mean Field Games system into a system of two coupled kinetic Fokker-Planck equations and an existence result for the latter system, obtaining consequently a solution for the Mean Field Games system.…”

Section: Numerical Methods Simulations and Control For Particles Dynamicsmentioning

confidence: 99%

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Differential Models, Numerical Simulations and Applications

Bretti

2021

Axioms

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Differential models, numerical methods and computer simulations play a fundamental role in applied sciences. Since most of the differential models inspired by real world applications have no analytical solutions, the development of numerical methods and efficient simulation algorithms play a key role in the computation of the solutions to many relevant problems. Moreover, since the model parameters in mathematical models have interesting scientific interpretations and their values are often unknown, estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In this respect, this Special Issue collects some important developments in different areas of application.

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Section: Numerical Methods Simulations and Control For Particles Dynamicsmentioning

confidence: 99%

“…Modeling and numerical methods for traffic [5,6] and manufacturing problems [7]. 3. Inverse problems for biomedical applications [8,9].…”

Section: Special Issue Overviewmentioning

confidence: 99%

Differential Models, Numerical Simulations and Applications

Bretti

2021

Axioms

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“…A kind of partial information nonzero-sum differential games with mean-field backward doubly stochastic differential equations is introduced in [23]. The MFG model based on a controlled Langevin equation is considered in [24]. The authors of [25] extend the theory of deterministic mean-field/aggregative games to multipopulation games.…”

Section: Introductionmentioning

confidence: 99%

Mean field games of energy storage devices: A finite difference analysis

Liu

Wei

et al. 2023

Asian Journal of Control

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This paper considers a mean field game of energy storage devices (ESDs) in power systems, where electrovalency is affected by the storage population. The competition processes of ESDs are characterized by a pair of coupled partial differential equations (PDEs). The so‐called mean field equilibrium (MFE) is obtained by resolving the PDEs. The resulting MFE strategy is then broadcast to all local controllers in order to independently determine a control input for each device. Since PDEs are difficult to be explicitly calculated, a pair of difference schemes are designed for approximating the exact solutions of the PDEs. Then the sufficient condition of stability is analyzed. Based on the proposed difference schemes, a difference iterative scheme is designed for numerically calculating the MFE. Some simulation results show the effectiveness of the proposed iterative schemes.

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Weak and Renormalized Solutions to a Hypoelliptic Mean Field Games System

Mimikos-Stamatopoulos

2024

SIAM J. Math. Anal.

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A Quadratic Mean Field Games Model for the Langevin Equation

Cited by 3 publications

References 15 publications

Differential Models, Numerical Simulations and Applications

Differential Models, Numerical Simulations and Applications

Mean field games of energy storage devices: A finite difference analysis

Weak and Renormalized Solutions to a Hypoelliptic Mean Field Games System

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