时隙ALOHA协议下的网络化控制系统协同设计
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摘要
针对网络化控制系统中信道容量有限的问题,本文提出一种基于时隙ALOHA通信协议的控制与通信协同设计方法.将控制系统的采样周期划分为若干等长度的时隙,在每个时隙中,系统的分布式传感器通过时隙ALOHA协议来随机竞争接入网络.由于在不同的采样周期各个传感器的接入状态不同,整个状态反馈控制系统将在若干子系统之间进行切换.据此,本文建立了离散的切换系统模型,并利用分段李雅普诺夫函数方法和平均驻留时间技术得到了能够保证系统指数稳定的充分条件.然后,给出能够保证控制系统稳定所需的信道吞吐率的界限,进而得到了时隙ALOHA协议中的最大重传次数与控制系统衰减率的定量关系.通过上述方法,本文建立了控制-通信协同设计的框架结构,可将控制器的增益矩阵和时隙ALOHA通信协议进行协同设计.最后,通过仿真验证了本文所提出的协同设计方法的有效性.
Considering that the communication channel of networked control systems(NCSs)is capacity limited,this paper investigates a control-communication co-design problem by using the slotted ALOHA protocol.Each sampling time interval is divided into several time slots,in each of which the distributed sensors randomly contend to access the communication channel based on the slotted ALOHA protocol.As the access states of the sensors change in different sampling time periods,the closed-loop NCSs switch among subsystems that are modeled from the original NCSs.Accordingly,a discrete time switch system model is built in this paper,and sufficient conditions that can ensure the exponential stability of the NCS s are derived by applying the piecewise Lyapunov function method and the average dwell time approach.Then,the lower bound of the communication throughput to guarantee the exponential stability of the NCSs is provided.Moreover,the quantitative relation between the maximum number of retransmissions in the slotted ALOHA protocol and the attenuation rate of the NCSs is derived.Based on these results,a control-communication co-design method is proposed such that the control gain matrix and the slotted ALOHA protocol can be designed simultaneously.Finally,a numerical simulation example illustrates the effectiveness of the proposed co-design method.
Considering that the communication channel of networked control systems(NCSs)is capacity limited,this paper investigates a control-communication co-design problem by using the slotted ALOHA protocol.Each sampling time interval is divided into several time slots,in each of which the distributed sensors randomly contend to access the communication channel based on the slotted ALOHA protocol.As the access states of the sensors change in different sampling time periods,the closed-loop NCSs switch among subsystems that are modeled from the original NCSs.Accordingly,a discrete time switch system model is built in this paper,and sufficient conditions that can ensure the exponential stability of the NCS s are derived by applying the piecewise Lyapunov function method and the average dwell time approach.Then,the lower bound of the communication throughput to guarantee the exponential stability of the NCSs is provided.Moreover,the quantitative relation between the maximum number of retransmissions in the slotted ALOHA protocol and the attenuation rate of the NCSs is derived.Based on these results,a control-communication co-design method is proposed such that the control gain matrix and the slotted ALOHA protocol can be designed simultaneously.Finally,a numerical simulation example illustrates the effectiveness of the proposed co-design method.
引文
[1]FAN Jialu,JIANG Yi,CHAI Tianyou.Operational feedback control of industrial processes in a wireless network environment.Acta Automatica Sinica,2016,42(8):1 166-1 174.(范家璐,姜艺,柴天佑.无线网络环境下工业过程运行反馈控制方法.自动化学报,2016,42(8):1166-1174.)
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[3]WANG Li,LI Dai,HE Zhonghe,et al.Urban traffic network control based on cluster consensus of multi-agent systems.Control Theory&Applications,2014,31(1 1):1448-1456.(王力,李岱,何忠贺,等.基于多智能体分群同步的城市路网交通控制.控制理论与应用,2014,31(11):1448-1456.)
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[7]WALSH G,YE H.Scheduling of networked control systems.IEEE Control Systems Magazine,2001,21(1):57-65.
[8]WALSH G,BELDIMAN O,BUSHNELL L.Asymptotic behaviour of nonlinear networked control systems.IEEE Transactions on Automnatic Control,2001,46(7):1093-1097.
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[10]ZAALOUL A,AATTAR M B and HANINI M,et al.Sharing channel in IEEE 802.16 using the cooperative model of slotted ALOHA.In ternational Journal of Computer&Organization Trends,20 1 3,3(9):439-443.
[11]GHEZ S,VERDU S,SCHWARTZ S.Stability properties of slotted ALOHA with multipacket reception cap ability.IEEE Transactions on Automatic Control,1988,33(7):640-649.
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[13]KWAK B,SONG N,MILLER L E.Performance analysis of exponential backoff.IEEE Transactions on Networking,2005,13(2):343-355.
[14]LIU K,FRIDMAN E,JOHANSSON K H.Networked control with stochastic scheduling.IEEE Transactions on Automatic Control,2015,60(11):3071-3076.
[15]LIU K,FRIDMAN E,JOHANSSON K H.Networked control with a stochastic scheduling:a time-delay approach.Proceedings of the19th International Federation of Automatic Control.Langford Lane,UK:Elsevier,2014:6484-6489.
[16]SUI T,YOU K,FU M.Optimal sensor scheduling for state estimation over lossy channel.IET Control Theory and Applications,2015,9(16):2458-2465.
[17]FAROKHI F,JOHANSSON K H.Stochastic sensor scheduling for networked control systems.IEEE Transactions on Automatic Con trol 2014.59(5):1147-1162.
[18]HAN D,WU J,ZHANG H,et al.Optimal sensor scheduling for multiple linear dynamical systems.Automatica,2017,75(C):260-270.
[19]HAN D,MO Y,WU J,et al.Stochastic event-triggered sensor schedule for remote state estimation.IEEE Transactions on Automatic Control,2015,60(10):2661-2675.
[20]ZHANG C,JIA Y.Distributed estimation for stochastic hybrid systems with event-triggered sensor schedule.IET Control Theory and Applications,2017,1 1(2):173-181.
[21]TATIKONDA S,MITTER S.Control under communication constraints.IEEE Transactions on Automatic Control,2004,49(7):1056-1067.
[22]TATIKONDA S,MITTER S.Control over noisy channels.IEEE Transactions on Networking,2004,49(7):1 196-1200.
[23]WEN S,GUO G,WONG W.Hybrid event-time-triggered networked control systems:scheduling-event-control co-design.Information Sciences,2015,305:269-284.
[24]LIN H,ANTSAKLIS P J.Stability and persistent disturbance attenuation properties for a class of networked control systems:Switched system approach.International Journal of Control,2005,78(18):1447-1458.
[25]YU M,WANG L,XIE G M,et al.Stabilization of networked control systems with data packet dropout via switched system approach.Proceedings of the 43rd IEEE Conference on Decision and Control.Atlantis,Paradise Island,B ahamas:IEEE,2004:3539-3544.
[26]ZHANG W,YU L.Output feedback stabilization of networked control systems with packet dropouts.IEEE Transactions on Automatic Control,2007,52(9):1705-1710.
[27]ROM R,SIDI M.Multiple Access Protocols:Performance and Analysis.New York:Springer-Verlag,1990:47-74.
[28]YANG Y.Delay distributions of slotted ALOHA and CSMA.IEEE Transactions on Communications,2003,5 1(1 1):1 846-1857.
[29]GHAOUI L E,OUSTRY F,AITRAMI M.A cone complementarity linearization algorithm for static output feedback and related problems.IEEE Transactions on Automatic Control,1997,42(8):1 17 1-1176.
[30]LIAN F L.Analysis,design,modeling and control of networked con trol system.Michigan:Department of Mechanical Engineering,Uni versity of Michigan,2001.
[2]CLOETE N,MALEKIAN R,NAIR L.Design of smart sensors for real-time water quality monitoring.IEEE Access,2016,4:3975-3990.
[3]WANG Li,LI Dai,HE Zhonghe,et al.Urban traffic network control based on cluster consensus of multi-agent systems.Control Theory&Applications,2014,31(1 1):1448-1456.(王力,李岱,何忠贺,等.基于多智能体分群同步的城市路网交通控制.控制理论与应用,2014,31(11):1448-1456.)
[4]TANENBAUM A S.Computer Networks.Upper Saddle River:Prentice Hall,2003:135-138.
[5]TAB BARA M,NESIC D,TEEL A.Input-output stability of wireless networked control systems.Proceedings of the 44th IEEE Conference Decision and Control.Seville,Spain:IEEE,2005:209-214.
[6]NESIC D,TEEL A.Input-output stability properties of networked control systems.IEEE Transactions on Automatic Control,2004,49(10):1650-1667.
[7]WALSH G,YE H.Scheduling of networked control systems.IEEE Control Systems Magazine,2001,21(1):57-65.
[8]WALSH G,BELDIMAN O,BUSHNELL L.Asymptotic behaviour of nonlinear networked control systems.IEEE Transactions on Automnatic Control,2001,46(7):1093-1097.
[9]CARLEIAL A,HELLMAN M E.Bistable behavior of ALOHA-type systems.IEEE Transactions on Communications,1975,23(4):40 1-410.
[10]ZAALOUL A,AATTAR M B and HANINI M,et al.Sharing channel in IEEE 802.16 using the cooperative model of slotted ALOHA.In ternational Journal of Computer&Organization Trends,20 1 3,3(9):439-443.
[11]GHEZ S,VERDU S,SCHWARTZ S.Stability properties of slotted ALOHA with multipacket reception cap ability.IEEE Transactions on Automatic Control,1988,33(7):640-649.
[12]TOBAGI F A.Multiaccess protocols in packet communication systems.IEEE Transactions on Communications,1980,28(4):1-21.
[13]KWAK B,SONG N,MILLER L E.Performance analysis of exponential backoff.IEEE Transactions on Networking,2005,13(2):343-355.
[14]LIU K,FRIDMAN E,JOHANSSON K H.Networked control with stochastic scheduling.IEEE Transactions on Automatic Control,2015,60(11):3071-3076.
[15]LIU K,FRIDMAN E,JOHANSSON K H.Networked control with a stochastic scheduling:a time-delay approach.Proceedings of the19th International Federation of Automatic Control.Langford Lane,UK:Elsevier,2014:6484-6489.
[16]SUI T,YOU K,FU M.Optimal sensor scheduling for state estimation over lossy channel.IET Control Theory and Applications,2015,9(16):2458-2465.
[17]FAROKHI F,JOHANSSON K H.Stochastic sensor scheduling for networked control systems.IEEE Transactions on Automatic Con trol 2014.59(5):1147-1162.
[18]HAN D,WU J,ZHANG H,et al.Optimal sensor scheduling for multiple linear dynamical systems.Automatica,2017,75(C):260-270.
[19]HAN D,MO Y,WU J,et al.Stochastic event-triggered sensor schedule for remote state estimation.IEEE Transactions on Automatic Control,2015,60(10):2661-2675.
[20]ZHANG C,JIA Y.Distributed estimation for stochastic hybrid systems with event-triggered sensor schedule.IET Control Theory and Applications,2017,1 1(2):173-181.
[21]TATIKONDA S,MITTER S.Control under communication constraints.IEEE Transactions on Automatic Control,2004,49(7):1056-1067.
[22]TATIKONDA S,MITTER S.Control over noisy channels.IEEE Transactions on Networking,2004,49(7):1 196-1200.
[23]WEN S,GUO G,WONG W.Hybrid event-time-triggered networked control systems:scheduling-event-control co-design.Information Sciences,2015,305:269-284.
[24]LIN H,ANTSAKLIS P J.Stability and persistent disturbance attenuation properties for a class of networked control systems:Switched system approach.International Journal of Control,2005,78(18):1447-1458.
[25]YU M,WANG L,XIE G M,et al.Stabilization of networked control systems with data packet dropout via switched system approach.Proceedings of the 43rd IEEE Conference on Decision and Control.Atlantis,Paradise Island,B ahamas:IEEE,2004:3539-3544.
[26]ZHANG W,YU L.Output feedback stabilization of networked control systems with packet dropouts.IEEE Transactions on Automatic Control,2007,52(9):1705-1710.
[27]ROM R,SIDI M.Multiple Access Protocols:Performance and Analysis.New York:Springer-Verlag,1990:47-74.
[28]YANG Y.Delay distributions of slotted ALOHA and CSMA.IEEE Transactions on Communications,2003,5 1(1 1):1 846-1857.
[29]GHAOUI L E,OUSTRY F,AITRAMI M.A cone complementarity linearization algorithm for static output feedback and related problems.IEEE Transactions on Automatic Control,1997,42(8):1 17 1-1176.
[30]LIAN F L.Analysis,design,modeling and control of networked con trol system.Michigan:Department of Mechanical Engineering,Uni versity of Michigan,2001.