基于切换系统理论的混杂交通系统特性分析
发布时间：2019-04-12 20:16
【摘要】：基于数学模型的交通运输系统的预测、分析与控制一直以来都是交通运输领域研究的主要方法和关注的热点。交通系统在不同程度上都体现出“混杂”的特性,是一类典型的混杂动态系统。目前研究表明,混杂系统理论是研究交通系统性质和运动规律的有效工具,但是主要的成果还集中在如混杂Petri网、混杂自动机等以离散事件为基础的模型上,而对连续变量的运动规律以及相关的系统性质的研究和认识还较少。切换系统模型适宜于研究混杂交通系统的连续变量运动规律,但是在交通系统中的应用却很少,其主要原因是现有常用的各种切换系统的Lyapunov研究方法并不适用于混杂交通系统,这也是目前切换系统理论在混杂交通系统中应用的“瓶颈”所在。本文针对目前切换系统理论在混杂交通系统中应用存在的问题,创造性地提出了驻留时间依赖Lyapunov函数方法,并在此基础上分析研究了混杂交通系统的稳定性、耗散性以及有界性等系统的基本性质,并应用到了典型的混杂交通系统的分析与设计中。具体来讲,本文的研究工作主要有以下几个方面：(1)将一类常见的Multi-phase交通控制系统建模为时间依赖切换系统模型,并分别提出连续时间与离散时间情形下的驻留时间依赖Lyapunov函数方法。详细讨论了所有Phase均稳定,稳定与不稳定Phase均存在,及所有Phase均不稳定三种情况下的稳定性分析问题,得出了三种情况下系统渐近稳定的充分条件。特别值得指出的是,驻留时间依赖Lyapunov函数方法能够有效地处理所有Phase均不稳定这一Multi-phase交通系统特有的情况,解决了传统Lyapunov函数方法在混杂交通系统应用中的“瓶颈”问题。最后通过在环岛交通控制系统与过饱和交叉口控制系统的应用,验证了本文方法的有效性。(2).运用驻留时间依赖Lyapunov函数方法,进一步研究了连续时间与离散时间Multi-phase交通系统的耗散性。给出了非线性切换系统一个形式简洁的耗散性充分条件,并将其应用到了分析Multi-phase交通系统的(Q,S,R)耗散性中,得出了所有Phase都稳定情形下系统(Q,S,R)耗散的充分条件。而后特别研究了所有Phase都不稳定情形,考虑了L2稳定性(l2稳定性)分析问题。值得指出的是,对于切换系统,即使所有子系统都是稳定的,其L2稳定性(l2稳定性)分析仍然是一个尚未完全解决的问题。本文提出的驻留时间依赖Lyapunov函数方法为该难题提供了一种简单易行的解决的方案,定量地给出了驻留时间与L2增益(l2增益)之间的关系,并且应用到了Multi-phase交通系统耗散性分析问题中。(3)研究了含不确定性的混杂交通系统的稳定性与耗散性分析问题。由于实际的交通系统在建模的过程中不可避免的存在不确定性,因此有必要将驻留时间依赖Lyapunov函数法推广到含不确定性的混杂交通控制系统中。分别得到了连续时间与离散时间不确定Multi-phase交通控制系统L2稳定(l2稳定)的充分条件以及渐近稳定的推论。另外,对于一类含有多胞不确定性的系统,发展出了参数及驻留时间依赖Lyapunov函数方法,用于降低结论的保守性,并给出了参数依赖状态反馈控制器的设计方法,应用到了交通流不确定情况下的过饱和信号交叉口控制中。(4)研究了混杂交通系统的有界性问题。基于有限时间稳定性与有限时间有界概念,研究了连续时间与离散时间Multi-phase交通系统的状态有界性问题。基于驻留时间依赖Lyapunov函数方法,给出了系统有限时间有界的充分条件,以及得出了保证系统有限时间稳定的推论,并且能够通过求解一组优化问题估计Multi-phase交通控制系统状态最小边界。而后还特别考虑状态依赖混杂交通控制系统的有限时间有界性分析问题,利用多Lyapunov函数方法得到了保证此类系统有限时间有界的充分条件,并进一步考虑了有限时间H∞性能分析问题。基于所得的分析结论,还研究了有限时间有界反馈控制器的设计问题。最后,将有界性分析结论分别应用到了环岛交通控制系统、过饱和交叉口控制系统与匝道信号控制系统中。
[Abstract]:The prediction, analysis and control of the transportation system based on the mathematical model has been the main method and focus of the research in the field of transportation. The traffic system embodies the characteristics of the "confounders" in different degrees, and is a kind of typical hybrid dynamic system. The present study shows that the hybrid system theory is an effective tool for studying the nature and the motion law of the traffic system, but the main results are also on the model based on discrete events such as hybrid Petri net, hybrid automatic machine, etc. And the research and recognition of the motion law of the continuous variable and the related system property are less. The model of the switching system is suitable for studying the continuous variable movement of the hybrid traffic system, but the application in the traffic system is very low, and the main reason is that the Lyapunov method of the various switching systems used in the prior art is not applicable to the hybrid traffic system, This is also the "Bottleneck" of the application of the current switching system theory in hybrid traffic system. In the light of the existing problems of the current switching system theory in hybrid traffic system, a method of resident time-dependent Lyapunov function is creatively proposed, and the basic properties of the system such as the stability, the dissipation and the boundedness of the hybrid traffic system are analyzed. And is applied to the analysis and design of a typical hybrid traffic system. In particular, the research work in this paper mainly includes the following aspects: (1) modeling a class of common multi-phase traffic control systems as time-dependent switching system models, and respectively presenting the dwell time dependent Lyapunov function method in the case of continuous time and discrete time. In this paper, the stability, stability and unstable phase of all the Pase are discussed in detail, and the stability analysis of all the Pase is not stable. The sufficient conditions for the asymptotic stability of the system are obtained. In particular, it is worth noting that the resident time-dependent Lyapunov function method can effectively handle the situation peculiar to the multi-phase traffic system, and solves the "Bottleneck" problem of the traditional Lyapunov function method in the application of the hybrid traffic system. Finally, the effectiveness of this method is verified by the application of the control system of the traffic control system of the ring island and the super-saturated intersection. (2). The dissipation of the continuous time and the discrete-time multi-phase transport system is further studied by means of the time-dependent Lyapunov function method. The sufficient conditions for the dissipation of the system (Q, S, R) of the multi-phase transport system (Q, S, R) are obtained, and the sufficient conditions for the dissipation of the system (Q, S, R) in the case of the stability of all the Pase are obtained. The stability of L2 stability (l2 stability) was considered. It is worth noting that for a switching system, even if all subsystems are stable, its L2 stability (l2 stability) analysis remains a problem that has not yet been fully resolved. The residence time-dependent Lyapunov function method presented in this paper provides a simple and easy solution for this problem. The relationship between the dwell time and the L2 gain (l2 gain) is given quantitatively, and the problem of the dissipative analysis of the multi-phase traffic system is also applied. (3) The stability and dissipation of the hybrid traffic system with uncertainty are studied. Because of the inevitable uncertainty of the actual traffic system in the process of modeling, it is necessary to extend the resident time-dependent Lyapunov function method to the uncertain hybrid traffic control system. The sufficient conditions for the stability of the multi-phase traffic control system (L2) and the asymptotic stability of the multi-phase traffic control system (L2) are obtained. In addition, for a class of system with multi-cell uncertainty, the method of parameter and residence time-dependent Lyapunov function is developed to reduce the conservativeness of the conclusion, and the design method of the parameter-dependent state feedback controller is given. And is applied to the control of the supersaturated signal intersection under the uncertain condition of the traffic flow. (4) The boundedness of hybrid traffic system is studied. Based on the finite-time stability and the finite time-bounded concept, the state-bounded problem of the continuous time and the discrete-time multi-phase traffic system is studied. Based on the time-dependent Lyapunov function method, a sufficient condition for the finite time-bounded system of the system is given, and the inference of the system's finite time stability is obtained, and the state minimum boundary of the multi-phase traffic control system can be estimated by solving a set of optimization problems. In addition, the finite-time boundedness analysis of the state-dependent hybrid traffic control system is also considered, and the sufficient conditions for the finite time-bounded of such systems are obtained by using the multi-Lyapunov function method, and the problem of the finite-time H-level performance analysis is further considered. Based on the results of the analysis, the design of the finite-time bounded feedback controller is also studied. Finally, the boundedness analysis is applied to the loop island traffic control system, the oversaturated intersection control system and the ramp signal control system, respectively.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：U491
本文编号：2457358
[Abstract]:The prediction, analysis and control of the transportation system based on the mathematical model has been the main method and focus of the research in the field of transportation. The traffic system embodies the characteristics of the "confounders" in different degrees, and is a kind of typical hybrid dynamic system. The present study shows that the hybrid system theory is an effective tool for studying the nature and the motion law of the traffic system, but the main results are also on the model based on discrete events such as hybrid Petri net, hybrid automatic machine, etc. And the research and recognition of the motion law of the continuous variable and the related system property are less. The model of the switching system is suitable for studying the continuous variable movement of the hybrid traffic system, but the application in the traffic system is very low, and the main reason is that the Lyapunov method of the various switching systems used in the prior art is not applicable to the hybrid traffic system, This is also the "Bottleneck" of the application of the current switching system theory in hybrid traffic system. In the light of the existing problems of the current switching system theory in hybrid traffic system, a method of resident time-dependent Lyapunov function is creatively proposed, and the basic properties of the system such as the stability, the dissipation and the boundedness of the hybrid traffic system are analyzed. And is applied to the analysis and design of a typical hybrid traffic system. In particular, the research work in this paper mainly includes the following aspects: (1) modeling a class of common multi-phase traffic control systems as time-dependent switching system models, and respectively presenting the dwell time dependent Lyapunov function method in the case of continuous time and discrete time. In this paper, the stability, stability and unstable phase of all the Pase are discussed in detail, and the stability analysis of all the Pase is not stable. The sufficient conditions for the asymptotic stability of the system are obtained. In particular, it is worth noting that the resident time-dependent Lyapunov function method can effectively handle the situation peculiar to the multi-phase traffic system, and solves the "Bottleneck" problem of the traditional Lyapunov function method in the application of the hybrid traffic system. Finally, the effectiveness of this method is verified by the application of the control system of the traffic control system of the ring island and the super-saturated intersection. (2). The dissipation of the continuous time and the discrete-time multi-phase transport system is further studied by means of the time-dependent Lyapunov function method. The sufficient conditions for the dissipation of the system (Q, S, R) of the multi-phase transport system (Q, S, R) are obtained, and the sufficient conditions for the dissipation of the system (Q, S, R) in the case of the stability of all the Pase are obtained. The stability of L2 stability (l2 stability) was considered. It is worth noting that for a switching system, even if all subsystems are stable, its L2 stability (l2 stability) analysis remains a problem that has not yet been fully resolved. The residence time-dependent Lyapunov function method presented in this paper provides a simple and easy solution for this problem. The relationship between the dwell time and the L2 gain (l2 gain) is given quantitatively, and the problem of the dissipative analysis of the multi-phase traffic system is also applied. (3) The stability and dissipation of the hybrid traffic system with uncertainty are studied. Because of the inevitable uncertainty of the actual traffic system in the process of modeling, it is necessary to extend the resident time-dependent Lyapunov function method to the uncertain hybrid traffic control system. The sufficient conditions for the stability of the multi-phase traffic control system (L2) and the asymptotic stability of the multi-phase traffic control system (L2) are obtained. In addition, for a class of system with multi-cell uncertainty, the method of parameter and residence time-dependent Lyapunov function is developed to reduce the conservativeness of the conclusion, and the design method of the parameter-dependent state feedback controller is given. And is applied to the control of the supersaturated signal intersection under the uncertain condition of the traffic flow. (4) The boundedness of hybrid traffic system is studied. Based on the finite-time stability and the finite time-bounded concept, the state-bounded problem of the continuous time and the discrete-time multi-phase traffic system is studied. Based on the time-dependent Lyapunov function method, a sufficient condition for the finite time-bounded system of the system is given, and the inference of the system's finite time stability is obtained, and the state minimum boundary of the multi-phase traffic control system can be estimated by solving a set of optimization problems. In addition, the finite-time boundedness analysis of the state-dependent hybrid traffic control system is also considered, and the sufficient conditions for the finite time-bounded of such systems are obtained by using the multi-Lyapunov function method, and the problem of the finite-time H-level performance analysis is further considered. Based on the results of the analysis, the design of the finite-time bounded feedback controller is also studied. Finally, the boundedness analysis is applied to the loop island traffic control system, the oversaturated intersection control system and the ramp signal control system, respectively.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：U491
【参考文献】
相关期刊论文 前2条
1 赵晓华,陈阳舟;基于混杂系统理论的单交叉口信号灯控制[J];北京工业大学学报;2004年04期
2 倪金;陈阳舟;张利国;李宏峰;;两相邻路口的混杂自动机模型与信号协调控制[J];交通信息与安全;2011年03期
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