TY - GEN

T1 - Discrete-time decentralized control using the risk-sensitive performance criterion in the large population regime

T2 - 2015 American Control Conference, ACC 2015

AU - Moon, Jun

AU - Basar, Tamer

N1 - Publisher Copyright:
© 2015 American Automatic Control Council.

PY - 2015/7/28

Y1 - 2015/7/28

N2 - This paper considers a discrete-time decentralized control problem using the risk-sensitive cost function when there is a large number of agents. We solve this problem via mean field control theory. We first obtain an individual robust decentralized controller that is a function of the local state information and a bias term that is related to the mean field term. We then construct an auxiliary system that characterizes the best approximation to the mean field term in the mean-square sense when the number of agents, say N, goes to infinity. We prove that the set of individual decentralized controllers is an ε-Nash equilibrium, where ε can be made arbitrarily close to zero when N → ∞. Finally, we show that in view of the relationship with risk-sensitive, H∞, and LQG control, the equilibrium features robustness, and converges to that of the LQG mean field game when the risk-sensitivity parameter goes to infinity.

AB - This paper considers a discrete-time decentralized control problem using the risk-sensitive cost function when there is a large number of agents. We solve this problem via mean field control theory. We first obtain an individual robust decentralized controller that is a function of the local state information and a bias term that is related to the mean field term. We then construct an auxiliary system that characterizes the best approximation to the mean field term in the mean-square sense when the number of agents, say N, goes to infinity. We prove that the set of individual decentralized controllers is an ε-Nash equilibrium, where ε can be made arbitrarily close to zero when N → ∞. Finally, we show that in view of the relationship with risk-sensitive, H∞, and LQG control, the equilibrium features robustness, and converges to that of the LQG mean field game when the risk-sensitivity parameter goes to infinity.

UR - http://www.scopus.com/inward/record.url?scp=84940953076&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940953076&partnerID=8YFLogxK

U2 - 10.1109/ACC.2015.7172082

DO - 10.1109/ACC.2015.7172082

M3 - Conference contribution

AN - SCOPUS:84940953076

T3 - Proceedings of the American Control Conference

SP - 4779

EP - 4784

BT - ACC 2015 - 2015 American Control Conference

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 1 July 2015 through 3 July 2015

ER -