Feedback Control Theory for Dynamic Traffic Assignment

ISBN-13: 9781447112099 / Angielski / Miękka / 2011 / 207 str.

Pushkin Kachroo; Kaan Ozbay

Opis

The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology impacts all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies, ...., new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series offers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. Micro-technology and modern communications technology are revolutionising many aspects of our daily lives and so it is not surprising that it is impacting societal transportation systems whether our highways, airways, seaways or railways. The Advances in Industrial Control series reported on these developments for long haul railway systems in a monograph by Howlett and Pudney (ISBN 3-S40-19990-X, 1995). Now it is the turn of transportation in a contribution from Pushkin Kachroo and Kaan Ozbay. The authors viewpoint is that this new set of transportation problems are control problems and that control engineers should be highly active in this field. Their volume covers all the aspects of modelling, problem formulation, and applies various control methodologies to solve the control problems formulated.

Spis treści

1 Introduction.- Objectives.- 1. Dynamic Traffic Routing.- Objectives.- Control Algorithm Design.- Sensing.- Actuation.- Automatic Control vs. Human-in-the-loop Control.- Overall System.- Traffic Analysis Notation.- 2. Motivation.- 3. Literature Review.- 4. FeedBack Control.- Control Design Steps.- Feedback Control Example.- Other Issues.- 5. Summary.- 6. Exercises.- Questions.- Problems.- 7. References.- 2 Traffic Flow Theory.- Objectives.- 1. Introduction.- 2. Conservation Law.- 3. Traffic Density-Flow Relationships.- Greenshield’s Model [1].- Greenberg Model [2]:.- Underwood Model [3]:.- Northwestern University Model [4]:.- Drew Model [5]:.- Pipes- Munjal Model [6]:.- Multiregime Models [7]:.- Diffusion Models:.- 4 Microscopic Traffic Characteristics [17,18,19].- 5 Traffic Model.- 6 Classification of PDEs[20,21,22].- Variables.- Order of the PDE.- Linearity.- Boundary Conditions.- 7 Existence of Solution [21].- Traffic Problem.- 8 Method of Characteristics to Solve First Order PDEs [20].- 9. Traffic Shock Wave Propagation.- 10. Traffic Measurements.- Time mean speed.- Space mean speed.- Time Headway.- Space Headway.- Flow measurements.- Traffic Density Measurements.- Occupancy.- Distributed Measurements.- Moving Observer Method.- 11. Summary.- 12. Exercises.- Questions.- Problems.- 13. References.- 3 Modeling and Problem Formulation.- Objectives.- 1. Introduction.- 2. System Dynamics.- 3. Feedback Control for the Traffic as a Distributed Parameter System.- DTR Formulation.- 4. Discretized System Dynamics.- 5. Feedback Control for the Traffic as a Lumped Parameter System.- DTR Formulation.- 6. Sample Problem for Space Discretized Dynamics.- 7. Sample Problem For Space and Time Discretized Dynamics: Three Alternate Routes Case Description.- System Dynamics.- System Analysis.- Simple Feedback Control Law.- Description of the Results for Different Scenarios.- 8. Summary.- 9. Exercises.- Questions.- Problems.- 10. References.- 4 Dynamic Traffic Routing Problem in Distributed Parameter Setting.- Objectives.- 1. Introduction.- 2. System Dynamics.- 3. Sliding Mode Control.- 4. Chattering Reduction.- 5. Numerical Examples.- 6. Generalization of Chattering Reduction Results.- 7. Control Design for DTR Problem.- 8. Numerical Solution of Traffic PDE.- Finite Difference Approximation.- 9. Error Analysis.- Boundary Conditions.- 10. Simulation Software.- 11. Simulation Results.- 12. Summary.- 13. Exercises.- Questions.- Problems.- 14. References.- 5 Dynamic Traffic Routing Problem in Distributed Parameter Setting Using Semigroup Theory.- Objectives.- 1. Introduction.- 2. Mathematical Preliminaries.- Basic Topology.- Vector Space.- Normed Linear Space.- Sequences.- Cauchy Sequence.- Banach Space.- Inner Product Space.- Hilbert Space.- Sobolev Space.- Semigroups.- 3. System Dynamics.- 4. Existing Work.- 5. Summary.- 6. Exercises.- Questions.- Problems.- 7. References.- 6 Fuzzy Feedback Control for Dynamic Traffic Routing.- Objectives.- 1. Introduction.- 2. Overview of Fuzzy Logic.- Crisp Sets.- Function Name.- Representation.- Function Name.- Representation.- Function Name.- Representation.- Fuzzy Sets.- 3. Sample Problem.- System Dynamics.- Simple Fuzzy Feedback Control Law.- Results & Description for different scenarios.- 4. Summary.- 5. Exercises.- Questions.- Problems.- 6. References.- 7 Feedback Control for Dynamic Traffic Routing in Lumped Parameter Setting.- Objectives.- 1. Introduction.- Notation.- 2. System Dynamics and DTR Problem.- DTR Formulation.- 3. Feedback Linearization Technique.- 4. Sample Problem (Two Alternate Routes with One Section Each).- 5. Sample Problem (Two Alternate Routes with Two Section Each).- 6. Solution for The One-Origin, One-Destination Case With Multiple Routes With Multiple Sections.- 7. Simulations.- Simulation environment.- 8. Sliding Mode Control for Point Diversion.- Sample Problem (Two alternate routes with one section).- Sample Problem (Two alternate routes with two section).- Solutions for the Generalized DTR Problem for Multiple Routes with Multiple Sections.- Simulation.- 9. Summary.- 10. Exercises.- Questions.- Problems.- 8 Feedback Control for Network Level Dynamic Traffic Routing.- Objectives.- 1. Introduction.- 2. System Description.- System Network.- System Dynamics.- 3. Dynamic Traffic Assignment Problem.- DTA Problem using Link Based Model.- DTA Problem using Route Based Model.- Feedback Control for the Traffic.- 4. Sample Problem.- System Network.- System Dynamics.- Feedback Control Design.- 5. Summary.- 6. Exercises.- Questions.- Problems.- 7. References.

Blurb

Traditionally, traffic assignment and traffic control in general have mostly been performed using optimisation techniques which do not lend themselves to real-time control. This volume presents feedback control techniques for performing traffic assignment in real-time, where traffic diversion control variables are instantaneous functions of sensed traffic variables.

The authors outline the whole theory behind Intelligent Transportation Systems (ITS) which allows traffic variables to be sensed in real-time and microprocessors to use the sensed traffic variable input to perform the traffic actuation tasks. They show how to design feedback controllers to perform dynamic traffic routing and assignment, and present the theory of feedback control as applied to this problem, with many new approaches for solving it.

Not only is the theory presented but a wide range of information on applications in terms of simulations and deployment. It is a valuable contribution to the subject, and will be of great use to researchers and all those with an interest in traffic control, including professional from highway administration and all those working in this industry.

 

Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.