TY - GEN
T1 - Solving LQ stochastic control and defining the controllability Gramian through kernel methods
AU - Aubin-Frankowski, Pierre Cyril
AU - Bensoussan, Alain
N1 - Publisher Copyright:
© 2025 IEEE.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - We introduce a reproducing kernel approach to the linear-quadratic (LQ) stochastic control problem, where control affects both drift and volatility. Unlike previous methods, our framework extends the controllability Gramian to general stochastic systems. Existing approaches, such as that of Liu and Peng [1], force to restrict to scalar noise and full control on volatility. Our method removes these limitations, establishing a direct link between deterministic and stochastic Gramians.
AB - We introduce a reproducing kernel approach to the linear-quadratic (LQ) stochastic control problem, where control affects both drift and volatility. Unlike previous methods, our framework extends the controllability Gramian to general stochastic systems. Existing approaches, such as that of Liu and Peng [1], force to restrict to scalar noise and full control on volatility. Our method removes these limitations, establishing a direct link between deterministic and stochastic Gramians.
UR - https://www.scopus.com/pages/publications/105031877352
U2 - 10.1109/CDC57313.2025.11312637
DO - 10.1109/CDC57313.2025.11312637
M3 - Conference contribution
AN - SCOPUS:105031877352
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5463
EP - 5468
BT - 2025 IEEE 64th Conference on Decision and Control, CDC 2025
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 64th IEEE Conference on Decision and Control, CDC 2025
Y2 - 9 December 2025 through 12 December 2025
ER -