基于切換系統(tǒng)理論的混雜交通系統(tǒng)特性分析
發(fā)布時(shí)間：2019-04-12 20:16
【摘要】：基于數(shù)學(xué)模型的交通運(yùn)輸系統(tǒng)的預(yù)測(cè)、分析與控制一直以來都是交通運(yùn)輸領(lǐng)域研究的主要方法和關(guān)注的熱點(diǎn)。交通系統(tǒng)在不同程度上都體現(xiàn)出“混雜”的特性,是一類典型的混雜動(dòng)態(tài)系統(tǒng)。目前研究表明,混雜系統(tǒng)理論是研究交通系統(tǒng)性質(zhì)和運(yùn)動(dòng)規(guī)律的有效工具,但是主要的成果還集中在如混雜Petri網(wǎng)、混雜自動(dòng)機(jī)等以離散事件為基礎(chǔ)的模型上,而對(duì)連續(xù)變量的運(yùn)動(dòng)規(guī)律以及相關(guān)的系統(tǒng)性質(zhì)的研究和認(rèn)識(shí)還較少。切換系統(tǒng)模型適宜于研究混雜交通系統(tǒng)的連續(xù)變量運(yùn)動(dòng)規(guī)律,但是在交通系統(tǒng)中的應(yīng)用卻很少,其主要原因是現(xiàn)有常用的各種切換系統(tǒng)的Lyapunov研究方法并不適用于混雜交通系統(tǒng),這也是目前切換系統(tǒng)理論在混雜交通系統(tǒng)中應(yīng)用的“瓶頸”所在。本文針對(duì)目前切換系統(tǒng)理論在混雜交通系統(tǒng)中應(yīng)用存在的問題,創(chuàng)造性地提出了駐留時(shí)間依賴Lyapunov函數(shù)方法,并在此基礎(chǔ)上分析研究了混雜交通系統(tǒng)的穩(wěn)定性、耗散性以及有界性等系統(tǒng)的基本性質(zhì),并應(yīng)用到了典型的混雜交通系統(tǒng)的分析與設(shè)計(jì)中。具體來講,本文的研究工作主要有以下幾個(gè)方面：(1)將一類常見的Multi-phase交通控制系統(tǒng)建模為時(shí)間依賴切換系統(tǒng)模型,并分別提出連續(xù)時(shí)間與離散時(shí)間情形下的駐留時(shí)間依賴Lyapunov函數(shù)方法。詳細(xì)討論了所有Phase均穩(wěn)定,穩(wěn)定與不穩(wěn)定Phase均存在,及所有Phase均不穩(wěn)定三種情況下的穩(wěn)定性分析問題,得出了三種情況下系統(tǒng)漸近穩(wěn)定的充分條件。特別值得指出的是,駐留時(shí)間依賴Lyapunov函數(shù)方法能夠有效地處理所有Phase均不穩(wěn)定這一Multi-phase交通系統(tǒng)特有的情況,解決了傳統(tǒng)Lyapunov函數(shù)方法在混雜交通系統(tǒng)應(yīng)用中的“瓶頸”問題。最后通過在環(huán)島交通控制系統(tǒng)與過飽和交叉口控制系統(tǒng)的應(yīng)用,驗(yàn)證了本文方法的有效性。(2).運(yùn)用駐留時(shí)間依賴Lyapunov函數(shù)方法,進(jìn)一步研究了連續(xù)時(shí)間與離散時(shí)間Multi-phase交通系統(tǒng)的耗散性。給出了非線性切換系統(tǒng)一個(gè)形式簡(jiǎn)潔的耗散性充分條件,并將其應(yīng)用到了分析Multi-phase交通系統(tǒng)的(Q,S,R)耗散性中,得出了所有Phase都穩(wěn)定情形下系統(tǒng)(Q,S,R)耗散的充分條件。而后特別研究了所有Phase都不穩(wěn)定情形,考慮了L2穩(wěn)定性(l2穩(wěn)定性)分析問題。值得指出的是,對(duì)于切換系統(tǒng),即使所有子系統(tǒng)都是穩(wěn)定的,其L2穩(wěn)定性(l2穩(wěn)定性)分析仍然是一個(gè)尚未完全解決的問題。本文提出的駐留時(shí)間依賴Lyapunov函數(shù)方法為該難題提供了一種簡(jiǎn)單易行的解決的方案,定量地給出了駐留時(shí)間與L2增益(l2增益)之間的關(guān)系,并且應(yīng)用到了Multi-phase交通系統(tǒng)耗散性分析問題中。(3)研究了含不確定性的混雜交通系統(tǒng)的穩(wěn)定性與耗散性分析問題。由于實(shí)際的交通系統(tǒng)在建模的過程中不可避免的存在不確定性,因此有必要將駐留時(shí)間依賴Lyapunov函數(shù)法推廣到含不確定性的混雜交通控制系統(tǒng)中。分別得到了連續(xù)時(shí)間與離散時(shí)間不確定Multi-phase交通控制系統(tǒng)L2穩(wěn)定(l2穩(wěn)定)的充分條件以及漸近穩(wěn)定的推論。另外,對(duì)于一類含有多胞不確定性的系統(tǒng),發(fā)展出了參數(shù)及駐留時(shí)間依賴Lyapunov函數(shù)方法,用于降低結(jié)論的保守性,并給出了參數(shù)依賴狀態(tài)反饋控制器的設(shè)計(jì)方法,應(yīng)用到了交通流不確定情況下的過飽和信號(hào)交叉口控制中。(4)研究了混雜交通系統(tǒng)的有界性問題�；谟邢迺r(shí)間穩(wěn)定性與有限時(shí)間有界概念,研究了連續(xù)時(shí)間與離散時(shí)間Multi-phase交通系統(tǒng)的狀態(tài)有界性問題。基于駐留時(shí)間依賴Lyapunov函數(shù)方法,給出了系統(tǒng)有限時(shí)間有界的充分條件,以及得出了保證系統(tǒng)有限時(shí)間穩(wěn)定的推論,并且能夠通過求解一組優(yōu)化問題估計(jì)Multi-phase交通控制系統(tǒng)狀態(tài)最小邊界。而后還特別考慮狀態(tài)依賴混雜交通控制系統(tǒng)的有限時(shí)間有界性分析問題,利用多Lyapunov函數(shù)方法得到了保證此類系統(tǒng)有限時(shí)間有界的充分條件,并進(jìn)一步考慮了有限時(shí)間H∞性能分析問題�；谒玫姆治鼋Y(jié)論,還研究了有限時(shí)間有界反饋控制器的設(shè)計(jì)問題。最后,將有界性分析結(jié)論分別應(yīng)用到了環(huán)島交通控制系統(tǒng)、過飽和交叉口控制系統(tǒng)與匝道信號(hào)控制系統(tǒng)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.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：U491
本文編號(hào)：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.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：U491
【參考文獻(xiàn)】
相關(guān)期刊論文 前2條
1 趙曉華,陳陽舟;基于混雜系統(tǒng)理論的單交叉口信號(hào)燈控制[J];北京工業(yè)大學(xué)學(xué)報(bào);2004年04期
2 倪金;陳陽舟;張利國(guó);李宏峰;;兩相鄰路口的混雜自動(dòng)機(jī)模型與信號(hào)協(xié)調(diào)控制[J];交通信息與安全;2011年03期
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