Robust linear quadratic mean field social control: A direct approach

Tinghan Xie; Bing Chang Wang; Jianhui Huang

doi:10.1051/cocv/2021021

Robust linear quadratic mean field social control: A direct approach

Tinghan Xie, Bing Chang Wang, Jianhui Huang

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

This paper investigates a robust linear quadratic mean field team control problem. The model involves a global uncertainty drift which is common for a large number of weakly-coupled interactive agents. All agents treat the uncertainty as an adversarial agent to obtain a "worst case"disturbance. The direct approach is applied to solve the robust social control problem, where the state weight is allowed to be indefinite. Using variational analysis, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) and the centralized controls which contain the population state average. Then the decentralized feedback-type controls are designed by mean field heuristics. Finally, the relevant asymptotically social optimality is further proved under proper conditions.

Original language	English
Article number	2021021
Pages (from-to)	1-19
Number of pages	19
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	27
DOIs	https://doi.org/10.1051/cocv/2021021
Publication status	Accepted/In press - 12 Feb 2021

Keywords

Forward-backward stochastic differential equation
Linear quadratic control
Mean field game
Model uncertainty
Social optimality

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization
Computational Mathematics

More information

10.1051/cocv/2021021

Cite this

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title = "Robust linear quadratic mean field social control: A direct approach",

abstract = "This paper investigates a robust linear quadratic mean field team control problem. The model involves a global uncertainty drift which is common for a large number of weakly-coupled interactive agents. All agents treat the uncertainty as an adversarial agent to obtain a {"}worst case{"}disturbance. The direct approach is applied to solve the robust social control problem, where the state weight is allowed to be indefinite. Using variational analysis, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) and the centralized controls which contain the population state average. Then the decentralized feedback-type controls are designed by mean field heuristics. Finally, the relevant asymptotically social optimality is further proved under proper conditions. ",

keywords = "Forward-backward stochastic differential equation, Linear quadratic control, Mean field game, Model uncertainty, Social optimality",

author = "Tinghan Xie and Wang, {Bing Chang} and Jianhui Huang",

note = "Funding Information: ∗The first author acknowledges the financial support from: P0008686, P0031044. The second author acknowledges the support from: NNSF of China (61773241), the Youth Innovation Group Project of Shandong University (2020QNQT016). The third author acknowledges the support from: RGC 153005/14P, 153275/16P, P0030808. The authors also acknowledge the support from: The PolyU-SDU Joint Research Centre on Financial Mathematics. Publisher Copyright: {\textcopyright} EDP Sciences, SMAI 2021.",

year = "2021",

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language = "English",

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AU - Xie, Tinghan

AU - Wang, Bing Chang

AU - Huang, Jianhui

N1 - Funding Information: ∗The first author acknowledges the financial support from: P0008686, P0031044. The second author acknowledges the support from: NNSF of China (61773241), the Youth Innovation Group Project of Shandong University (2020QNQT016). The third author acknowledges the support from: RGC 153005/14P, 153275/16P, P0030808. The authors also acknowledge the support from: The PolyU-SDU Joint Research Centre on Financial Mathematics. Publisher Copyright: © EDP Sciences, SMAI 2021.

PY - 2021/2/12

Y1 - 2021/2/12

N2 - This paper investigates a robust linear quadratic mean field team control problem. The model involves a global uncertainty drift which is common for a large number of weakly-coupled interactive agents. All agents treat the uncertainty as an adversarial agent to obtain a "worst case"disturbance. The direct approach is applied to solve the robust social control problem, where the state weight is allowed to be indefinite. Using variational analysis, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) and the centralized controls which contain the population state average. Then the decentralized feedback-type controls are designed by mean field heuristics. Finally, the relevant asymptotically social optimality is further proved under proper conditions.

AB - This paper investigates a robust linear quadratic mean field team control problem. The model involves a global uncertainty drift which is common for a large number of weakly-coupled interactive agents. All agents treat the uncertainty as an adversarial agent to obtain a "worst case"disturbance. The direct approach is applied to solve the robust social control problem, where the state weight is allowed to be indefinite. Using variational analysis, we first obtain a set of forward-backward stochastic differential equations (FBSDEs) and the centralized controls which contain the population state average. Then the decentralized feedback-type controls are designed by mean field heuristics. Finally, the relevant asymptotically social optimality is further proved under proper conditions.

KW - Forward-backward stochastic differential equation

KW - Linear quadratic control

KW - Mean field game

KW - Model uncertainty

KW - Social optimality

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DO - 10.1051/cocv/2021021

M3 - Journal article

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SP - 1

EP - 19

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

SN - 1292-8119

M1 - 2021021

ER -

Robust linear quadratic mean field social control: A direct approach

Abstract

Keywords

ASJC Scopus subject areas

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