A Feedback-Type Optimal Solution for Partially-Observed Linear-Quadratic Risk-Sensitive Optimal Control Problem of Mean-Field Type Stochastic Systems

• 成果类型: Article
• 署名作者: Oh, Yuna; Moon, Jun
• 署名单位: Hanyang University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3545701
• 发表日期: 2025
• 页码: 5452-5459
• 关键词: STOCHASTIC PROCESSES; optimal control; Noise measurement; PROCESS CONTROL; mathematical models; filtration; training; Symmetric matrices; Stochastic systems; State estimation; Mean-field type stochastic systems; optimal estimation; partially observed risk-sensitive stochastic control

摘要

We study the linear-quadratic (LQ) risk-sensitive optimal control problem for mean-field type stochastic differential equations (MF-SDEs) driven by Brownian motion. The expected values of state and control variables are included in the MF-SDE as well as the objective functional, and the objective functional is of the risk-sensitive type. The control has access to the noisy state information from the mean-field type stochastic observation model. Under this setting, we obtain the practically implementable explicit feedback-type linear optimal solution to the problem. In particular, we decompose the original problem into the (control-constrained) partially observed LQ risk-sensitive control problem and the LQ risk-neutral problem for the mean-field dynamics. While the optimal solution of the former is characterized by the risk-sensitive state estimator and satisfies the associated control constraint, the optimal solution of the latter is represented by the state-feedback mean-field type process. Then, by combining the optimal solutions of these two problems, we obtain the explicit feedback-type linear optimal solution to the original problem. We provide the simulation results of the modified national income problem to demonstrate that our feedback-type optimal solution is practically implementable.