Energy-Optimal Control in Transportation Systems

Abstract

A task is to control one vehicle along a given track within the prescribed travel time. An optimal solution of this elementary control task can be found by several methods: experimentally, using Pontryagin’s maximum principle, dynamical programming or numerical methods- An original control algorithm is presented in the paper. It is proposed εs an adaptive algorithm, which means the results of the last run are checked and only some changes of the last control are made to get better results in the next run. The algorithm has three parts: the first for an accurate reaching of the final point, the second for calculation of the optimal maximum speed. The third part of the algorithm divides the total travel time into the parts of a track in the optimal way. The form of the optimal trajectory was proved by all the methods enumerated above. The control rule in each part of the trajectory is known which makes possible a completely straightforfard automatic implementation. Hence the optimal control task is changed to the task of finding the instants of switching the control from one part of the trajectory to the next one. As for the inherent, theory the algorithm is based on changing a system of differential equations describing the movement of a vehicle onto a system of equations in variations. The algorithm v/as tested on a simulation model of a tractive vehicle programmed on a digital computer. The results were encouraging: savings were attained in energy consumption and the calculation was fast and accurate enough. Further efforts will be made to modify the algorithm for the control in real time operation.