The individual time trial as an optimal control problem
Jenny De Jong (Universiteit Utrecht)
Robbert Fokkink (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Geert Jan Olsder (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Arend Schwab (TU Delft - Mechanical Engineering)
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Abstract
In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and
involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial.
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