Energy optimal control to approach traffic lights

In this paper energy optimal solutions for the approach of red traffic lights are derived. As cars waste most of the fuel in city traffic and especially in queuing at traffic lights, the presented framework provides solutions to save fuel and to protect the environment. The solutions are obtained using the definition of spent physical work which has to be minimized. It covers both cases, that the time of switching of the traffic lights is known and that the time of switching can only be modeled as a stochastic process. For a known time of switching a continuous solution is derived using Pontryagin Minimum Principle; in the stochastic case a modified Bellmann equation is formulated. The latter is solved with dynamic programming techniques. The presented solutions can be used for autonomous driving as well as for driving assistant systems. Simulation results show the potential savings using the presented approach.