Analysis of necessary conditions for the optimal control of a train

Fuel costs and gas emissions are a major concern for §transport operators. The rail freight industry must §curb rapidly rising fuel costs if it wishes to §remain competitive. Researchers at UniSA have been §studying the problem of determining driving §strategies that minimise fuel use. Their research §has led to the development of in-cab system that §helps drivers stay on time and reduce energy use. A §critical part of constructing an optimal strategy is §determining where the control should be changed. §Switching points are normally determined from §necessary conditions derived via the Pontryagin §Principle. In this book we use perturbation analysis §to develop an alternative form for the necessary §conditions for an optimal strategy over a steep §section of track. The new conditions show that the §optimal strategy involves a local trade-off between §energy used and time taken on each steep section. §They have also allowed us to develop more efficient §numerical calculation algorithms. Mathematicians, §engineers and rail operators will find this book a §useful reference for their interests in developing §sustainable technologies for rail.