TY - GEN
T1 - Risk-sensitive mean-field-type control
AU - Bensoussan, Alain
AU - Djehiche, Boualem
AU - Hamidou, Tembine
AU - Yam, Phillip
N1 - Funding Information:
The first author is supported by grants from the National Science Foundation (1303775 and 1612880), the Research Grants Council of the Hong Kong Special Administrative Region (City U 500113 and 11303316). The research of the second author is supported by grants from the Swedish Research Council. The research of the third author is supported by U.S. Air Force Office of Scientific Research under grant number FA9550-17-1-0259.
Funding Information:
ACKNOWLEDGEMENT The first author is supported by grants from the National Science Foundation (1303775 and 1612880), the Research Grants Council of the Hong Kong Special Administrative Region (City U 500113 and 11303316). The research of the second author is supported by grants from the Swedish Research Council. The research of the third author is supported by U.S. Air Force Office of Scientific Research under grant number FA9550-17-1-0259.
Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/28
Y1 - 2017/6/28
N2 - We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the risk-sensitive cost functional is also of mean-field type. We derive optimality equations in infinite dimensions connecting dual functions associated with Bellman functional to the adjoint process of the Pontryagin maximum principle. The case of linear-exponentiated quadratic cost and its connection with the risk-neutral solution is discussed.
AB - We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the risk-sensitive cost functional is also of mean-field type. We derive optimality equations in infinite dimensions connecting dual functions associated with Bellman functional to the adjoint process of the Pontryagin maximum principle. The case of linear-exponentiated quadratic cost and its connection with the risk-neutral solution is discussed.
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U2 - 10.1109/CDC.2017.8263639
DO - 10.1109/CDC.2017.8263639
M3 - Conference contribution
AN - SCOPUS:85046143547
T3 - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
SP - 33
EP - 38
BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017
Y2 - 12 December 2017 through 15 December 2017
ER -