您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (11): 58-69.doi: 10.6040/j.issn.1671-9352.0.2022.315

• • 上一篇    

具有非对称信息控制器平均场系统的分散控制

刘志强,亓庆源*,苌庆   

  1. 青岛大学自动化学院复杂性科学研究所, 山东 青岛 266071
  • 发布日期:2022-11-10
  • 作者简介:刘志强(1997— ),男,硕士研究生,研究方向为随机系统的优化控制. E-mail:liuzq59@163.com*通信作者简介:亓庆源(1990— ),男,博士,副教授,硕士生导师,研究方向为随机控制与最优估计. E-mail:qiqy123@163.com
  • 基金资助:
    国家自然科学基金资助项目(61903210,61873179,U1806204,61922051);山东省自然科学基金资助项目(ZR2019BF002);中国博士后基金资助项目(2019M652324,2021T140354)

Decentralized control of mean-field systems with asymmetric information controllers

LIU Zhi-qiang, QI Qing-yuan*, CHANG Qing   

  1. Institute of Complexity Science, School of Automation, Qingdao University, Qingdao 266071, Shandong, China
  • Published:2022-11-10

摘要: 通过极大值原理以及解耦平均场正倒向随机微分方程法,解决了连续时间平均场系统的有限时间域非对称信息线性二次控制问题。最终得到了最优控制策略以及一组非对称Riccati型方程。

关键词: 平均场系统, 伊藤系统, 非对称信息, 极大值原理

Abstract: The finite horizon asymmetric information linear quadratic control problem for continuous-time mean-field systems is solved by the maximum principle and decoupled mean-field forward and backward stochastic differential equations. Eventually, the optimal control strategy and a set of asymmetric Riccati-type equations are obtained.

Key words: mean-field system, Itô, system, asymmetric information, maximum principle

中图分类号: 

  • O232
[1] KAC M. Foundations of kinetic theory[C] //Proceedings of the third Berkeley symposium on mathematical statistics and probability: Berkeley: University of California Press, 1956.
[2] MCKEAN H P. A class of Markov processes associated with nonlinear parabolic equations[J]. Proceedings of the National Academy of Sciences of the United States of America, 1966, 56(6):1907-1911.
[3] YONG J. Linear-quadratic optimal control problems for mean-field stochastic differential equations[J]. SIAM Journal on Control and Optimization, 2013, 51(4):2809-2838.
[4] ELLIOTT R, LI Xun, NI Yuanhua. Discrete time mean-field stochastic linear-quadratic optimal control problems[J]. Automatica, 2013, 49(11):3222-3233.
[5] ZHANG Huanshui, QI Qingyuan. Optimal control for mean-field system: discrete time case[C] // IEEE 55th Conference on Decision and Control.[S.l.] :[s.n.] , 2016: 4474-4480.
[6] QI Qingyuan, ZHANG Huanshui. Necessary and sufficient solution to optimal control for linear continuous time mean-field system[J]. IFAC-Papers On Line, 2017, 50(1):1495-1501.
[7] QI Qingyuan, ZHANG Huanshui, WU Zhen. Stabilization control for linear continuous time mean-field systems[J]. IEEE Transactions on Automatic Control, 2019, 64(8):3461-3468.
[8] ZHANG Huanshui, QI Qingyuan, FU Minyue. Optimal stabilization control for discrete time mean-field stochastic systems[J]. IEEE Transactions on Automatic Control, 2019, 64(3):1125-1136.
[9] QI Qingyuan, XIE Lihua, ZHANG Huanshui. Linear quadratic optimal control for discrete-time mean-field systems with input delay[J/OL]. IEEE Transactions on Automatic Control, doi:10.1109/TAC.2021.3106877.
[10] MA Xiao, QI Qingyuan, LI Xun, et al. Optimal control and stabilization for linear continuous time mean-field systems with delay[J]. IET Control Theory & Applications, 2022, 16(3):283-300.
[11] WITSENHAUSEN H. A counterexample in stochastic optimum control[J]. SIAM Journal on Control, 1968, 6(1):131-147.
[12] 徐娟娟. 时滞系统若干控制问题的研究[M]. 济南:山东大学出版社,2013. XU Juanjuan. Research on some control problems for linear systems with time-delay[M]. Jinan: Shandong University Press, 2013.
[13] NAYYAR A, GUPTA A, LANGBORT C, et al. Common information based Markov perfect equilibria for stochastic games with asymmetric information: finite games[J]. IEEE Transactions on Automatic Control, 2014, 59(3):555-570.
[14] GUPTA A, NAYYAR A, LANGBORT C, et al. Common information based Markov perfect equilibria for linear-Gaussian games with asymmetric information[J]. SIAM Journal on Control and Optimization, 2014, 52(5):3228-3260.
[15] ZHANG Huanshui,XU Juanjuan. Control for Itô stochastic systems with input delay[J]. IEEE Transactions on Automatic Control, 2017, 62(1):350-365.
[16] ASGHARI S, OUYANG Y, NAYYAR A. Optimal local and remote controllers with unreliable uplink channels[J]. IEEE Transactions on Automatic Control, 2019, 64(5):1816-1831.
[17] QI Qingyuan, XIE Lihua, ZHANG Huanshui. Optimal local and remote controls of networked systems: multiplicative noise case[C] // 2020 IEEE 16th International Conference on Control & Automation. [S.l.] : [s.n.] , 2020: 1179-1184.
[18] QI Qingyuan, XIE Lihua, ZHANG Huanshui. Optimal control for stochastic systems with multiple controllers of different information structures[J]. IEEE Transactions on Automatic Control, 2021, 66(9):4160-4175.
[19] AMOLD W, LAUB A. Generalized eigenproblem algorithms and software for algebraic Riccati equations[J]. Proceedings of the IEEE, 1984, 72(12):1746-1754.
[1] 苌庆,亓庆源,刘志强. 含有乘性噪声的理性期望模型的最优控制[J]. 《山东大学学报(理学版)》, 2022, 57(11): 50-57.
[2] 陈雨佳, 杨和. 一类三阶时滞微分方程在Banach空间中的周期解的存在性[J]. 山东大学学报(理学版), 2018, 53(8): 84-94.
[3] 张克勇1,2,周国华1. 非对称信息下闭环供应链差别定价协调机制[J]. J4, 2009, 44(2): 60-64.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!