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Congestion in traffic networks is a common issue in big cities and has considerable economic and environmental impacts. Traffic policies and real-time network management can reduce congestion using prediction of dynamical modeling. Initially, researchers studied traffic flow on a single road and then, they extended it to a network of roads. However, large-scale networks present challenges in terms of computation time and parameters' calibration. This led the researchers to focus on aggregated models and to look for a good balance between accuracy and practicality.One of the approaches describes traffic evolution with a continuous partial differential equation on a 2D-plane. Vehicles are represented by a two-dimensional density and their propagation is described by the flow direction. The thesis aims to develop these models and devises methods for their calibration and their validation. The contributions follow three extensions of the model.First, a simple model in two-dimensional space to describe a homogeneous network with a preferred direction of flow propagation is considered. A homogeneous network has the same speed limits and a similar concentration of roads everywhere. A method for validation using GPS probes from microsimulation is provided. Then, a space-dependent extension to describe a heterogeneous network with a preferred direction of flow propagation is presented. A heterogeneous network has different speed limits and a variable concentration of roads. Such networks are of interest because they can show how bottleneck affects traffic dynamics. Finally, the case of multiple directions of flow is considered using multiple layers of density, each layer representing a different flow direction. Due to the interaction between layers, these models are not always hyperbolic which can impact their stability.
This research is done in the context of European Research Council's Advanced Grant project Scale-FreeBack. The aim of Scale-FreeBack project is to develop a holistic scale-free control approach to complex systems, and to set new foundations for a theory dealing with complex physical networks with arbitrary dimension. One particular case is intelligent transportation systems that are capable to prevent the occurrence of congestions in rush hours. The contributions of the present PhD work are mainly related to traffic boundary control design and modelling on large-scale urban networks. We consider traffic from the macroscopic viewpoint describing it in terms of aggregated variables such as flow and density of vehicles, i.e., traffic is seen as a fluid whose motion is described using the concept of kinematic waves. The corresponding dynamic equation corresponds to a first-order hyperbolic partial differential equation. Within this PhD thesis, we propose control design techniques that completely rely on the intrinsic properties of the model. First of all, we solve one-dimensional (1D) boundary control problems, i.e., one road traffic. Thereby, the traffic state is driven to a space- and time-dependent desired trajectory that admits traffic regimes switching, i.e., both states can be partially congested and partially in the free-flow regime. This introduces non-linearities into the state equation, which we can handle and achieve the target by acting only from road's boundaries. Then, we extend the problem to a urban network of arbitrary size. The large-scale traffic dynamics are described by a two-dimensional (2D) conservation law model. The model parameters are defined everywhere in the continuum plane from its values on physical roads that are further interpolated as a function of distance to these roads. The traffic flow direction is determined by network's geometry (location of roads and intersections) and infrastructure parameters (speed limits, number of lanes, etc). This 2D model assumes that there exists a preferred direction of motion. For this case, we elaborate a unique method that considerably simplifies control design for traffic systems evolving in large-scale networks. In particular, we present a coordinate transformation that translates a 2D continuous traffic model into a continuous set of 1D systems equations. This enables an explicit elaboration of strategies for various control tasks to solve on large-scale networks: we design boundary control for 2D density in a mixed traffic regime, apply variable speed limit control to drive traffic to any space-dependent equilibrium, and calculate steady-states. Finally, we also present a new multi-directional two-dimensional continuous traffic model. This model is formally derived by solely using the demand-supply concept at one intersection (classical Cell Transmission Model). Our new model is called the NSWE-model, since it consists of four partial differential equations that describe the evolution of vehicle density with respect to cardinal directions: North, South, West and East. The traffic flow direction is determined by turning ratios at intersections. For this model, we design a boundary control that drives multi-directional congested traffic to a desired equilibrium vehicle density mitigating the congestion level. The effectiveness of our contributions were tested using simulated and real data. In the first case, the results are verified by using the well-known commercial traffic Aimsun, which produces microsimulations of vehicles' trajectories in a modelled network. In the second case, real data are obtained from sensors measuring traffic flow in the city of Grenoble, and collected using the Grenoble Traffic Lab.
In the past, the density-gradient term of second-order macroscopic models was replaced with a speed-gradient term to rectify the rearward movement of traffic waves. Hither, a classical speed-gradient macroscopic model is extended to account for the lateral flow dynamics on a multi-lane road. The anisotropic model is modified to capture some inherent vehicular multi-lane traffic features; lateral viscosity and velocity differentials. These variables are quantized within the scope of a two-dimensional spatial domain as opposed to the existing one-dimensional model. A detailed exemplification of acceleration and deceleration waves, stop-and-go waves, and cluster effects are presented to explain the path of information flow. All these non-linear flow properties are evident throughout the simulation.
This book gathers contributions on a variety of flowing collective systems. While primarily focusing on pedestrian dynamics, they also reflect the latest developments in areas such as vehicular traffic and granular flows and address related emerging topics such as self-propelled particles, data transport, swarm behavior, intercellular transport, and collective dynamics of biological systems. Combining fundamental research and practical applications in the various fields discussed, the book offers a valuable asset for researchers and practitioners alike.
This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods. The first part of the text is concerned with basic backstepping control of freeway traffic using the Aw-Rascle-Zhang (ARZ) second-order PDE model. It begins by illustrating a basic control problem – suppressing traffic with stop-and-go oscillations downstream of ramp metering – before turning to the more challenging case for traffic upstream of ramp metering. The authors demonstrate how to design state observers for the purpose of stabilization using output-feedback control. Experimental traffic data are then used to calibrate the ARZ model and validate the boundary observer design. Because large uncertainties may arise in traffic models, adaptive control and reinforcement learning methods are also explored in detail. Part II then extends the conventional ARZ model utilized until this point in order to address more complex traffic conditions: multi-lane traffic, multi-class traffic, networks of freeway segments, and driver use of routing apps. The final chapters demonstrate the use of the Lighthill-Whitham-Richards (LWR) first-order PDE model to regulate congestion in traffic flows and to optimize flow through a bottleneck. In order to make the text self-contained, an introduction to the PDE backstepping method for systems of coupled first-order hyperbolic PDEs is included. Traffic Congestion Control by PDE Backstepping is ideal for control theorists working on control of systems modeled by PDEs and for traffic engineers and applied scientists working on unsteady traffic flows. It will also be a valuable resource for researchers interested in boundary control of coupled systems of first-order hyperbolic PDEs.
This book gathers the carefully reviewed proceedings of the 19th International Conference on Systems Science, presenting recent research findings in the areas of Artificial Intelligence, Machine Learning, Communication/Networking and Information Technology, Control Theory, Decision Support, Image Processing and Computer Vision, Optimization Techniques, Pattern Recognition, Robotics, Service Science, Web-based Services, Uncertain Systems and Transportation Systems. The International Conference on Systems Science was held in Wroclaw, Poland from September 7 to 9, 2016, and addressed a range of topics, including systems theory, control theory, machine learning, artificial intelligence, signal processing, communication and information technologies, transportation systems, multi-robotic systems and uncertain systems, as well as their applications. The aim of the conference is to provide a platform for communication between young and established researchers and practitioners, fostering future joint research in systems science.