Robust Observability, Control, & Economics of Complex Cyber-Physical Networks

This dissertation deals with various aspects of cyber-physical system. As an example of cyber physical systems, we take transportation networks and solve various problems, namely: 1) Network Observability Problem, 2) Network Control Problem, and 3) Network Economics Problem. We have divided the dissertation into three parts which solve these three problems separately. First part of the dissertation presents a novel approach for studying the observability problem on a general network topology of a traffic network. We develop a new framework which investigates observability in terms of flow information on arcs and the routing information. Second part of the dissertation presents a feedback control design for a coordinated ramp metering problem for two consecutive on-ramps. We design a traffic allocation scheme for ramps based on Godunov’s numerical method and using distributed model. Third part of the dissertation presents a novel approach to model Vehicle Miles Traveled (VMT) dynamics and establish a methodology for designing an optimal VMT tax rate. An Optimal control problem is formulated by designing a cost function which aims to maximize the generated revenue while keeping the tax rate as low as possible. Using optimal control theory, a solution is provided to this problem. To the best knowledge of authors all the three problems have not been solved using the methods proposed in this dissertation, and hence they are a novel contribution to the field

Penetration effect of connected and automated vehicles on cooperative on‐ramp merging

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166263/1/itr2bf00795.pd

Design and Evaluate Coordinated Ramp Metering Strategies for Utah Freeways

MPC-641During the past few decades, ramp metering control has been widely implemented in many U.S. states, including Utah. Numerous studies and applications have demonstrated that ramp metering control is an effective strategy to reduce overall freeway congestion by managing the amount of traffic entering the freeway. Ramp metering controllers can be implemented as coordinated or uncoordinated systems. Currently, Utah freeway on-ramps are operated in an uncoordinated way. Despite improvements to the operational efficiency of mainline flows, uncoordinated ramp metering will inevitably create additional delays to the ramp flows. Therefore, this project aims to assist the Utah Department of Transportation (UDOT) in deploying coordinated ramp metering systems and evaluating the performance of deployed systems. First, we leverage a method to identify existing freeway bottlenecks using current UDOT datasets, including PeMs and ClearGuide. Based on this, we select the site that may benefit from coordinated ramp metering from those determined locations. A VISSIM model is then developed for this selected corridor and the VISSIM model is calibrated based on collected traffic flow data. We apply the calibrated VISSIM model to conduct simulations to evaluate system performance under different freeway mainline congestion levels. Finally, the calibrated VISSIM model is leveraged to evaluate the coordinated ramp metering strategy of the bottleneck algorithm from both operational and safety aspects

Complex Traffic Network Modeling & Area-wide Hierarchical Control

This thesis presents a novel methodology to divide a traffic region into subregions such that in each subregion a Macroscopic Fundamental Diagram (MFD) can be used to determine the state of that subregion. The region division is based on the theory of complex networks. We exploit the inherent network characteristics through PageRank centrality algorithm to identify the most significant nodes in the traffic network. We use these significant nodes as the seeds for a Voronoi diagram based partitioning mechanism of the network. A network wide hierarchical control framework is then presented which controls these sub regions individually and the network as a whole. At the subregion level a feedback controller is designed based on MFD concept. At the network level we develop a dynamic toll pricing algorithm to control the inflows into the network. This dynamic toll pricing is coupled with the subregion controller and thus forming a network wide hierarchical control. We use optimal control theory to design the dynamic toll pricing. A cost function is designed and then Hamilton-Jacobi-Bellman equation is used to derive an optimal control law that uses real-time information. The objective of the dynamic toll algorithm is to strike a balance between the toll price and optimal traffic conditions in each of the subregions. A case study is performed for the Manhattan area in New York city and results are provided through simulations

Inverse Problem for Non-viscous Mean Field Control: Example From Traffic

This thesis presents an inverse problem for mean field games where we find the mean field problem statement for which the given dynamics is the solution. We use distributed traffic as an example and derive the classic Lighthill Whitham Richards (LWR) model as a solution of the non-viscous mean field game. We also derive the same model by choosing a different problem where we use travel time, which is a distributed parameter, as the cost for the optimal control. We then study the stationary versions of these two problems and provide numerical solutions for the same

Control Problems for Conservation Laws with Traffic Applications

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks

Control Problems for Conservation Laws with Traffic Applications

Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks