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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (10): 53-63.doi: 10.6040/j.issn.1671-9352.0.2023.235

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具有同时丢包和延时的乘性噪声随机系统最优远近程控制

宋玉娇1(),亓庆源2,*()   

  1. 1. 青岛大学自动化学院, 山东 青岛 266071
    2. 哈尔滨工程大学青岛创新发展中心, 山东 青岛 266000
  • 收稿日期:2023-05-26 出版日期:2024-10-20 发布日期:2024-10-10
  • 通讯作者: 亓庆源 E-mail:songyj2021@163.com;qingyuan.qi@hrbeu.edu.cn
  • 作者简介:宋玉娇(1999—), 女, 硕士研究生, 研究方向为随机系统的优化控制. E-mail: songyj2021@163.com
  • 基金资助:
    国家自然科学基金资助项目(61903210);国家自然科学基金资助项目(61633014);国家自然科学基金资助项目(61873179)

Optimal local and remote control for multiplicative noise stochastic systems with packet loss and delay

Yujiao SONG1(),Qingyuan QI2,*()   

  1. 1. College of Automation, Qingdao University, Qingdao 266071, Shandong, China
    2. Qingdao Innovation and Development Center, Harbin Engineering University, Qingdao 266000, Shandong, China
  • Received:2023-05-26 Online:2024-10-20 Published:2024-10-10
  • Contact: Qingyuan QI E-mail:songyj2021@163.com;qingyuan.qi@hrbeu.edu.cn

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摘要：

研究了由远程控制器和近程控制器组成的乘性噪声随机系统的最优远近程控制问题。假设状态信息在通过上行信道时易发生丢失和延时, 而下行信道是完美的。首先, 利用凸变分技巧, 给出问题可解的充要条件, 并表明该最优远近程控制问题的可解性等价于一组正倒向随机差分方程的可解性。此外, 提出一种创新的分层控制算法, 利用配方法得到了反馈形式的最优控制策略。最后, 通过数值算例说明所得结果的有效性。

关键词: 最优远近程控制, 乘性噪声随机系统, 丢包和延时

Abstract:

The optimal local and remote control problem for a multiplicative noise stochastic system consisting of a remote controller and a local controller is investigated. It is assumed that the state information is prone to packet loss and delay when passing through the uplink channel, while the downlink channel is perfect. Firstly, the necessary and sufficient solvability conditions are developed by using the convex variational skill, which shows that the solvability of the optimal local and remote control problem is equivalent to the solvability of the forward and backward stochastic difference equations. Moreover, a novel hierarchical control algorithm is proposed, and the optimal feedback control strategy is obtained by using the complete square method. Finally, a numerical example is shown to illustrate the effectiveness of the obtained results.

Key words: optimal local and remote control, multiplicative noise stochastic system, packet loss and delay

中图分类号: 

  • O232

图1

具有丢包和延时的乘性噪声随机系统"

图2

E[xT(k)x(k)]轨迹仿真"

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