Characteristic Analysis For Hybrid Transportaion System Based On Switched System Theory

The prediction, analysis and control of transportation systems based on mathematical models have constantly been the main methods and focus of the study in the field of transportation. The transportation systems more or less exhibit the feature of "hybrid" to some extend, which implies transportation systems are a typical class of hybrid systems. Current research suggests, though, that hybrid system theory is an effective tool in investigating the properties of transportation systems and how they actually work, the major achievements are mainly obtained based on the modified models developed from discrete-event point of view, such as hybrid Petri network, hybrid automata and so on, however, the study and understanding of continuous variables in the system and related properties have been still insufficient so far. Although switched system model is suitable to study the continuous variable dynamics of hybrid transportation systems, the applications of switched system theory can be hardly found in study of transportation systems. The main reason is that the existing Lyapunov approaches commonly established for switched systems are not applicable for hybrid transportation systems, which is also the obvious "bottleneck" preventing hybrid transportation systems being served by switched system theory.Considering the present problem of application of switched system theory into hybrid transportation systems, a novel dwell time dependent Lyapunov function (DTDLF) approach is proposed in this thesis. Based on DTDLF, the basic properties of hybrid transportation systems including stability, dissipativity and boundedness have been analyzed, furthermore, the obtained results are capable to be applied into analysis and design for some typical hybrid transportation systems. Specially, the main contributions of this dissertation are summarized as what follows:(1) By modeling the common type of hybrid transportation system called Multi-phase transportation system as the time-dependent switched system, the DTDLF are constructed in continuous-time and discrete-time domains, respectively. The three cases, in which all phases are stable, stable and unstable phases both exist, and all phases are unstable, are considered. Sufficient conditions guaranteeing asymptotic stability are derived. It worth noting that DTDLF approach is able to deal with the particular situation with all phases unstable generated by Multi-phase transportation system, which can effectively solves the "bottleneck" problem caused by other existing Lyapunov methods. Finally, the proposed results have been validated by applying them into the roundabout traffic control system and over-saturated intersection traffic control system.(2) On the basis of DTDLF approach, the dissipativity of continuous-time and discrete-time Multi-phase transportation system has been further investigated. Simple sufficient conditions ensuring the nonlinear switched system dissipative are given, and they are applied into analyzing (Q, S, R) dissipativity of Multi-phase transportation system. Sufficient condition to guarantee the system with all phase stable (Q, S, R) dissipative is derived. Then, particularly considering the case with all phase unstable, the L2 stability (l2 stability) has been studied. It worth pointing out that, even all subsystems are stable, the L2 stability (l2 stability) analysis problem is still a challenging and unsolved problem for switched system, but the DTDLF approach proposed in this thesis provides us a simple and easy way to solve it. The relationship between dwell time and L2 gain (l2 gain) can be quantitatively characterized, and the obtained results are applied into dissipativity analysis of Multi-phase transportation system.(3) The stability and dissipativity of hybrid transportation system with uncertainties have been studied. Since the uncertainties inevitably exist in the mathematical models of actual transportation systems, it is necessary to extend DTDLF approach to analyze uncertain hybrid transportation systems. Sufficient conditions for ensuring the L2 stability (l2 stability) of continuous-time and discrete-time uncertain Multi-phase transportation systems are obtained along with corollaries about asymptotic stability, respectively. In addition, as to a class of uncertain systems with polytopic uncertainties, the parameter and dwell time dependent Lyapunov function approach is developed to reduce the conservativeness. The parameter dependent state feedback controller design is also considered, which can be applied into over-saturated intersection traffic control in presence of uncertain traffic flows.(4) The boundedness of hybrid transportation system has been investigated. Based on the concepts of finite-time stability and finite-time boundedness, the boundedness of state of Multi-phase transportation system in both continuous-time and discrete-time cases is considered. By exploiting DTDLF method, sufficient conditions for finite-time bounded and finite-time stability are obtained. Furthermore, the minimal state boundary of Multi-phase transportation can be estimated by solving a set of optimization problems. Then, the finite-time boundedness of a class of state-dependent hybrid transportation systems is taken into account. Sufficient conditions are derived based on multiple Lyapunov function approach, and finite-time H∞ performance is considered, based on which the finite-time state feedback control design problem is studied. In the end, the analysis results of finite-time boundedness are applied into roundabout traffic control system, over-saturated intersection traffic control system and ramping metering control system, respectively.