JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (10): 53-63.doi: 10.6040/j.issn.1671-9352.0.2023.235

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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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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

CLC Number: 

  • O232

Fig.1

The multiplicative noise stochastic system with packet loss and delay"

Fig.2

Trajectory simulation of E[xT(k)x(k)]"

1 SHIM D, KIM H, SASTRY S. Hierarchical control system synthesis for rotorcraft-based unmanned aerial vehicles[C]//AIAA Guidance, Navigation, and Control Conference and Exhibit. Renton, Virginia: Aerospace Press, 2000: 4057.
2 DING K , REN X , QUEVEDO D , et al. DoS attacks on remote state estimation with asymmetric information[J]. IEEE Transactions on Control of Network Systems, 2019, 6 (2): 653- 666.
doi: 10.1109/TCNS.2018.2867157
3 LIANG Xiao , XU Juanjuan , ZHANG Huanshui . Optimal control and stabilization for networked control systems with packet dropout and input delay[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2017, 64 (9): 1087- 1091.
4 NAYYAR A , MAHAJAN A , TENEKETZIS D . Decentralized stochastic control with partial history sharing: a common information approach[J]. IEEE Transactions on Automatic Control, 2013, 58 (7): 1644- 1658.
doi: 10.1109/TAC.2013.2239000
5 ASGHARI S M , OUYANG Y , NAYYAR A . Optimal local and remote controllers with unreliable uplink channels[J]. IEEE Transactions on Automatic Control, 2019, 64 (5): 1816- 1831.
doi: 10.1109/TAC.2018.2853807
6 AFSHARI M , MAHAJAN A . Optimal local and remote controllers with unreliable uplink channels: an elementary proof[J]. IEEE Transactions on Automatic Control, 2020, 65 (8): 3616- 3622.
doi: 10.1109/TAC.2019.2951658
7 OUYANG Y, ASGHARI S M, NAYYAR A. Optimal local and remote controllers with unreliable communication: the infinite horizon case[C]//Annual American Control Conference. New York: IEEE, 2018: 6634-6639.
8 LIANG Xiao , XU Juanjuan . Control for networked control systems with remote and local controllers over unreliable communication channel[J]. Automatica, 2018, 98, 86- 94.
doi: 10.1016/j.automatica.2018.09.015
9 JOSHI S M . On optimal control of linear systems in the presence of multiplicative noise[J]. IEEE Transactions on Aerospace and Electronic Systems, 1976, 12 (1): 80- 85.
10 ZHANG J , FRIDMAN E . Dynamic event-triggered control of networked stochastic systems with scheduling protocols[J]. IEEE Transactions on Automatic Control, 2021, 66 (12): 6139- 6147.
doi: 10.1109/TAC.2021.3061668
11 YANG Zaiyue , SHI Xiufang , CHEN Jiming . Optimal coordination of mobile sensors for target tracking under additive and multiplicative noises[J]. IEEE Transactions on Industrial Electronics, 2014, 61 (7): 3459- 3468.
doi: 10.1109/TIE.2013.2281157
12 LUO Yingting , ZHU Yunmin , LUO Dandan , et al. Globally optimal multisensor distributed random parameter matrices Kalman filtering fusion with applications[J]. Sensors, 2008, 8 (12): 8086- 8103.
doi: 10.3390/s8128086
13 TALEBI H A , KHORASANI K . A neural network-based multiplicative actuator fault detection and isolation of nonlinear systems[J]. IEEE Transactions on Control Systems Technology, 2013, 21 (3): 842- 851.
doi: 10.1109/TCST.2012.2186634
14 OUYANG Y , ASGHARI S M , NAYYAR A . Optimal infinite horizon decentralized networked controllers with unreliable communication[J]. IEEE Transactions on Automatic Control, 2020, 66 (4): 1778- 1785.
15 IMER O C , YÜKSEL S , BAŞAR T . Optimal control of LTI systems over unreliable communication links[J]. Automatica, 2006, 42 (9): 1429- 1439.
doi: 10.1016/j.automatica.2006.03.011
16 YONG Jiongmin . Linear-quadratic optimal control problems for mean-field stochastic differential equations[J]. SIAM Journal on Control and Optimization, 2013, 51 (4): 2809- 2838.
doi: 10.1137/120892477
17 QI Qingyuan , ZHANG Huanshui . Output feedback control and stabilization for networked control systems with packet losses[J]. IEEE Transactions on Cybernetics, 2017, 47 (8): 2223- 2234.
doi: 10.1109/TCYB.2016.2568218
18 ZHANG Qianqian , QI Qingyuan , TAN Cheng , et al. Decentralized control for multi-sensors networked systems with different transmission delays and packet dropouts[J]. Journal of the Franklin Institute, 2022, 359 (13): 6829- 6855.
doi: 10.1016/j.jfranklin.2022.06.045
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