Optimal driving strategy for a solar car on a level road

Every three years, solar cars from all over the world come toAustralia to participate in the World Solar Challenge. In 1993there were 52 cars in the race. Five cars finished within fivedays, each one breaking the previous race record and achievingan average speed exceeding 70 km/h. The performance of thesecars depends on many factors: power, aerodynamics, tractionefficiency, weight, reliability, and (not least of all) drivingstrategy. On a level road, the optimal driving strategy foran ideal car is essentially a speed-holding strategy. For areal car with inefficient energy storage, however, there aretwo distinct holding speeds. The lower speed is held when solarpower is low and must be supplemented from stored energy. Theupper speed is held when solar poler is high, and excess energyis stored.     

Optimal driving strategies for a train journey with non-zero track gradient and speed limits

In this paper we formulate and solve an important problem inapplied optimal control. A train is to be driven along a trackwith non-zero gradient, where speed limits are imposed. Thejourney is to be completed within a specified time using aslittle fuel as possible. We find key equations that determinestrategies of optimal type and present a general solution algorithm.Several specific examples will be given to illustrate the solutionprocedure.