外部扰动下一类车辆跟驰模型的稳定性分析
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摘要
为了研究交通拥堵问题,基于多智能体一致性理论对一类车辆跟驰模型的稳定性进行了研究.利用Lyapunov稳定性理论,通过设计适当的控制器使得车辆跟驰模型趋于稳定,并得到了模型稳定性的条件.此外,在车辆受到不确定的外部扰动的情形下,研究了车辆跟驰模型的稳定性.最后,采用Matlab仿真技术进行了数值模拟,结果表明在设计的控制器下,车辆跟驰模型快速趋于稳定,拥堵现象得到了有效的缓解.
In order to study the traffic jams and congestion,this paper investigated the stability of the car-following model on the basis of multi-agent consistency theory.By using Lyapunov stability theory,the car-following model is stabilized by designing appropriate controllers,and the stability conditions of the model are obtained.In addition,the stability of the car-following model is studied when the vehicle is subjected to uncertain external disturbances.Finally,the numerical simulation is implemented by using Matlab simulation technology.The results show that the car-following model is stabilized rapidly and the congestion phenomenon is effectively alleviated under the designed controller.
In order to study the traffic jams and congestion,this paper investigated the stability of the car-following model on the basis of multi-agent consistency theory.By using Lyapunov stability theory,the car-following model is stabilized by designing appropriate controllers,and the stability conditions of the model are obtained.In addition,the stability of the car-following model is studied when the vehicle is subjected to uncertain external disturbances.Finally,the numerical simulation is implemented by using Matlab simulation technology.The results show that the car-following model is stabilized rapidly and the congestion phenomenon is effectively alleviated under the designed controller.
引文
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[5] WANG J,RAKHA H A,FADHIOUN K.Validation of the Rakha-Pasumarthy-Adjerid car-following model for vehicle fuel consumption and emission estimation applications[J].Transportation Research Part D:Transport & Environment,2017,55:246-261.
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[18] LIN P,JIA Y,LI L.Distributed robustconsensus control in directed networks of agents with time-delay[J].Systems & Control Letters,2008,57(8):643-653.
[19] GU J Z,YANG H Y.Distributed adaptive control for multi-agent consensus with uncertainties[J].Chinese Journal of Engineering Mathematics,2012(5):741-748.
[20] ANDREASSON M,DIMAROGONAS D V,SANDBERG H,et al.Distributed control of networked dynamical systems:static feedback,integral action and consensus[J].IEEE Transactions on Automatic Control,2013,59(7):1750 - 1764.
[21] 曹伟俊.带有扰动的多智能体系统的一致性研究[D].北京:北京化工大学,2015.
[22] 宗鑫.随机时延二阶多智能体系统的一致性控制[D].临汾:山西师范大学,2016.
[23] 陈磊.不确定因素影响的多智能体系统跟踪控制方法研究[D].成都:电子科技大学,2017.
[24] NEWELL G F.Nonlinear effects in the dynamics of car following[J].Operations Research,1961,9(2):209-229.
[25] BANDO M,HASEBE K,NAKAYAMA A,et al.Dynamical model of traffic congestion and numerical simulation[J].Physical Review E,1995,51(2):1035-1042.
[2] CHAKROBORTY P,KIKUCHI S.Evaluation of the general motors based car-following models and a proposed fuzzy inference model[J].Transportation Research Part C:Emerging Technologies,1999,7(4):209-235.
[3] 陈晓强,孟建军,胥如迅,等.纯微观车辆跟驰行为研究与仿真[J].兰州交通大学学报,2014,33(6):123-126.
[4] KENDZIORRA A,WAGNER P,TOLEDO T.A stochastic car following model[J].Transportation Research Procedia,2016,15:198-207.
[5] WANG J,RAKHA H A,FADHIOUN K.Validation of the Rakha-Pasumarthy-Adjerid car-following model for vehicle fuel consumption and emission estimation applications[J].Transportation Research Part D:Transport & Environment,2017,55:246-261.
[6] ZHANG X,JARRETT D F.Stability analysis of the classical car-following model[J].Transportation Research Part B:Methodological,1997,31(6):441-462.
[7] HHIJBERTS H J C.Analysis of a continuous car-following model for a bus route:existence,stability and bifurcations of synchronous motions[J].Physica A:Statistical Mechanics & Its Applications,2002,308(1-4):489-517.
[8] SUN D H,LIAO X Y,PENG G H.Effect of looking backward on traffic flow in an extended multiple car-following model[J].Physica A:Statistical Mechanics & Its Applications,2011,390(4):631-635.
[9] CHEN D,LAVAL J,ZHENG Z,et al.A behavioral car-following model that captures traffic oscillations[J].Transportation Research Part B:Methodological,2012,46(6):744-761.
[10] LI S,YANG L,GAO Z,et al.Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers[J].ISA transactions,2014,53(6):1739-1745.
[11] YU S,SHI Z.An extended car-following model considering vehicular gap fluctuation[J].Measurement,2015,70:137-147.
[12] LI L,CHEN X,ZHANG L.A global optimization algorithm for trajectory data based car-following model calibration[J].Transportation Research Part C:Emerging Technologies,2016,68:311-332.
[13] 陈帝伊,杨朋超,马孝义,等.水轮机调节系统的混沌现象分析及控制[J].中国电机工程学报,2011,31(14):113-120.
[14] 陈帝伊,郑栋,马孝义,等.混流式水轮机调节系统建模与非线性动力学分析[J].中国电机工程学报,2012,32(32):116-123.
[15] 刘永忠.土质高边坡在饱和状态下的稳定性分析[J].兰州交通大学学报,2014(1):181-185.
[16] 陈帝伊,丁聪,把多铎,等.水轮发电机组系统的非线性建模与稳定性分析[J].水力发电学报,2014,33(2):235-241.
[17] 刘义才,刘斌,张永,等.具有双边随机时延和丢包的网络控制系统稳定性分析[J].控制与决策,2017,32(9):1565-1573.
[18] LIN P,JIA Y,LI L.Distributed robustconsensus control in directed networks of agents with time-delay[J].Systems & Control Letters,2008,57(8):643-653.
[19] GU J Z,YANG H Y.Distributed adaptive control for multi-agent consensus with uncertainties[J].Chinese Journal of Engineering Mathematics,2012(5):741-748.
[20] ANDREASSON M,DIMAROGONAS D V,SANDBERG H,et al.Distributed control of networked dynamical systems:static feedback,integral action and consensus[J].IEEE Transactions on Automatic Control,2013,59(7):1750 - 1764.
[21] 曹伟俊.带有扰动的多智能体系统的一致性研究[D].北京:北京化工大学,2015.
[22] 宗鑫.随机时延二阶多智能体系统的一致性控制[D].临汾:山西师范大学,2016.
[23] 陈磊.不确定因素影响的多智能体系统跟踪控制方法研究[D].成都:电子科技大学,2017.
[24] NEWELL G F.Nonlinear effects in the dynamics of car following[J].Operations Research,1961,9(2):209-229.
[25] BANDO M,HASEBE K,NAKAYAMA A,et al.Dynamical model of traffic congestion and numerical simulation[J].Physical Review E,1995,51(2):1035-1042.