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Stochastic LQ Control with Extra Measurability Restriction

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Different from the standard linear quadratic(LQ)problem for stochastic systems,the LQ problem considered in the paper has extra measurability restrictions.The problem also appears in the LQ control problem for stochastic systems with delays,rational expectations problems,asymmetric information control,and so on.The essential difficulty lies in that one has to optimize the input and its conditional expectations simultaneously.The stochastic maximum principle(SMP)and orthogo-nal decomposition technique are the key tools.Firstly,the authors establish the SMP and convert the original problem into forward and backward stochastic difference equations(FBSDEs)with extra measurability restrictions.Secondly,the authors resolve the FBSDEs by using the orthogonal decom-position technique and obtain the analytical solution to the underlying problem.Thirdly,the authors explore the essential distinction between the problem and the standard stochastic LQ control problem.Finally,numerical examples are given to illustrate the obtained results.

Multiplicative noise systemsoptimal controlstochastic maximum principlestochastic systems

WANG Hongxia、HU Yuxi、LI Zixing、SONG Lianfeng

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College of Electrical Engineering and Automation,Shandong University of Science and Technology,Qingdao 266590,China

Original Exploratory Program Project of National Natural Science Foundation of China国家自然科学基金Major Basic Research of Natural Science Foundation of Shandong ProvinceHigh-level Talent Team Project of Qingdao West Coast New Area

62250056U23A20325ZR2021ZD14RCTD-JC-2019-05

2024

10.1007/s11424-024-2501-0

系统科学与复杂性学报(英文版)
中国科学院系统科学研究所

系统科学与复杂性学报(英文版)

EI
影响因子：0.181
ISSN：1009-6124
年,卷(期)：2024.37(3)
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