Feedback Control Theory for Dynamic Traffic Assignment

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.