TY - JOUR
T1 - Social Optima in Robust Mean Field LQG Control
T2 - From Finite to Infinite Horizon
AU - Wang, Bing Chang
AU - Huang, Jianhui
AU - Zhang, Ji Feng
N1 - Funding Information:
Manuscript received November 7, 2018; revised August 2, 2019 and February 3, 2020; accepted May 14, 2020. Date of publication May 21, 2020; date of current version March 29, 2021. This work was supported in part by the National Key R&D Program of China under Grant 2018YFA0703800, in part by the National Natural Science Foundation of China under Grants 61773241 and 61877057, in part by RGC Grants P0030808 and P0005158, in part by the PolyU-SDU Joint Research Center on Financial Mathematics, and in part by the Youth Innovation Group Project of Shandong University under Grant 2020QNQT016. This paper was presented in part at the 2017 Asian Control Conference. (Corresponding author: Ji-Feng Zhang.) Bing-Chang Wang is with the School of Control Science and Engineering, Shandong University, Jinan 250061, China (e-mail: [email protected]).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/4
Y1 - 2021/4
N2 - This article studies social optimal control of mean field linear-quadratic-Gaussian models with uncertainty. Specially, the uncertainty is represented by an uncertain drift, which is common for all agents. A robust optimization approach is applied by assuming all agents treat the uncertain drift as an adversarial player. In our model, both dynamics and costs of agents are coupled by mean field terms, and both finite- and infinite-time horizon cases are considered. By examining social functional variation and exploiting person-by-person optimality principle, we construct an auxiliary control problem for the generic agent via a class of forward-backward stochastic differential equation system. By solving the auxiliary problem and constructing consistent mean field approximation, a set of decentralized control strategies is designed and shown to be asymptotically optimal.
AB - This article studies social optimal control of mean field linear-quadratic-Gaussian models with uncertainty. Specially, the uncertainty is represented by an uncertain drift, which is common for all agents. A robust optimization approach is applied by assuming all agents treat the uncertain drift as an adversarial player. In our model, both dynamics and costs of agents are coupled by mean field terms, and both finite- and infinite-time horizon cases are considered. By examining social functional variation and exploiting person-by-person optimality principle, we construct an auxiliary control problem for the generic agent via a class of forward-backward stochastic differential equation system. By solving the auxiliary problem and constructing consistent mean field approximation, a set of decentralized control strategies is designed and shown to be asymptotically optimal.
KW - Forward-backward stochastic differential equation (FBSDE)
KW - linear quadratic optimal control
KW - mean field control
KW - model uncertainty
KW - social functional variation
UR - http://www.scopus.com/inward/record.url?scp=85103320077&partnerID=8YFLogxK
U2 - 10.1109/TAC.2020.2996189
DO - 10.1109/TAC.2020.2996189
M3 - Journal article
AN - SCOPUS:85103320077
SN - 0018-9286
VL - 66
SP - 1529
EP - 1544
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 4
M1 - 9097879
ER -