Feedback Control for Network-Level Dynamic Traffic Routing

The aim of this chapter is to develop models for network-level traffic systems and, moreover, to design feedback controllers for network-level traffic problems in user-equilibrium as well as system-optimal settings. In order to do so, the chapter develops the network-level traffic dynamics for the traffic assignment problem and also shows the objective functions for the user-equilibrium and the system-optimal cases. Link-based and route-based models are presented from literature. Dynamic traffic assignment problem is formulated in the structure of an \(H_{\infty }\) control problem, so that the solution techniques available for the controller can be applied to the traffic assignment problem. A sample problem is presented and control design steps for that problem are presented.

[1]  E. G. Al'brekht.  On the optimal stabilization of nonlinear systems , 1961 .

[2]  J. Doyle,et al.  𝓗∞ Control of Nonlinear Systems via Output Feedback: Controller Parameterization , 1994, IEEE Trans. Autom. Control..

[3]  A. Isidori,et al.  H∞ control via measurement feedback for general nonlinear systems , 1995, IEEE Trans. Autom. Control..

[4]  I. Okutani.  THE KALMAN FILTERING APPROACHES IN SOME TRANSPORTATION AND TRAFFIC PROBLEMS , 1987 .

[5]  Arthur J. Krener.  Optimal Model Matching Controllers for Linear and Nonlinear Systems , 1992 .

[6]  J. Helton,et al.  H∞ control for nonlinear systems with output feedback , 1993, IEEE Trans. Autom. Control..

[7]  A. Schaft.  Nonlinear State Space H ∞ Control Theory , 1993 .

[8]  A. Friedman.  Differential games , 1971 .

[9]  J. Helton,et al.  H" CONTROL FOR NONLINEAR PLANTS: CONNECTIONS WITH DIFFERENTIAL GAMES , 1989 .

[10]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[11]  Markos Papageorgiou,et al.  Dynamic modeling, assignment, and route guidance in traffic networks , 1990 .

[12]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[13]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[14]  J. L. Mancilla Aguilar,et al.  Nonlinear observers , 1997 .

[15]  J. Helton,et al.  H/sup infinity / control for nonlinear plants: connections with differential games , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[16]  Kalidas Ashok,et al.  DYNAMIC ORIGIN-DESTINATION MATRIX ESTIMATION AND PREDICTION FOR REAL- TIME TRAFFIC MANAGEMENT SYSTEMS , 1993 .

[17]  J. Hedrick,et al.  Nonlinear Observers—A State-of-the-Art Survey , 1989 .