Dynamic Routing Problem in Distributed Parameter Setting

Abstract

The aim of this chapter is to design control law for the DTR (Dynamic Traffic Routing) problem modeled in the distributed parameter setting. For the control design, the chapter uses the sliding mode control technique for regulating the error. Sliding mode control provides a robust method against bounded uncertainties. The price to pay for that robustness is chattering. The chapter shows methods to deal with chattering reduction in the control implementation. Control design and its software simulation using sliding mode control are presented in this chapter. The chapter also provides a simple study of discretization errors that are obtained in the numerical approximation of the distributed model for software simulation. The chapter shows the development of a simple software simulation code and its simulation to study this problem.

The plots in Sect. 5.5 “Numerical Examples” and Sect. 5.6 “Generalization of Chattering Reduction Results” are ©1996 IEEE, having been adapted with permission from the paper by Pushkin Kachroo, and Masayoshi Tomizuka, “Chattering Reduction and Error Convergence in the Sliding Mode Control of a Class of Nonlinear Systems,” IEEE Transactions on Automatic Control, vol. 41, no. 7, July 1996, pp. 1063–1068, DOI: https://doi.org/10.1109/9.508917.

Section 5.7 “Control Design for DTR Problem” and Sect. 5.8 “Numerical Solution of Traffic PDE” are ©1997 IEEE, based on the paper by Pushkin Kachroo and Kaan Özbay, “Sliding Mode for User Equilibrium Dynamic Traffic Routing Control”, Proceedings of IEEE Conference on Intelligent Transportation Systems ITSC97, Boston, 1997, DOI: https://doi.org/10.1109/ITSC.1997.660452.