Optimal control using pontryagin's maximum principle and dynamic programming

This chapter describes the application of Pontryagin's Maximum Principle and Dynamic Programming for vehicle drivingwith minimum fuel consumption. The focus is on minimum-fuel accelerations. For the fuel consumption modeling, a six-parameter polynomial approximation is proposed. With the Maximum Principle, this consumption model yields optimal accelerations with a linearly decreasing acceleration as a function of the velocity. This linear acceleration behavior is also observed in real traffic situations by other researchers. Dynamic Programming is implemented with a backward recursion on a specially chosen distance grid. This grid enables the calculation of realistic gear shifting behaviour during vehicle accelerations. Gear shifting dynamics are taken into account. © 2010 Springer-Verlag London.