Optimal Pacing of a Cyclist in a Time Trial Based on Individualized Models of Fatigue and Recovery

Abstract

This article formulates the optimal pacing of a cyclist on hilly terrain time trials as a minimum-time optimal control problem. The maximal power of a cyclist serves as a time-varying constraint and depends on fatigue and recovery which are captured via dynamic models proposed early in the article. Experimental protocols for identifying the individualized parameters of the proposed fatigue and recovery models are detailed and results for six human subjects are shown. In an analytical treatment via necessary conditions of the Pontryagin minimum principle, we show that the cyclist’s optimal power in a time trial is limited to only four modes of all-out, coasting, pedaling at a critical power, or constant speed (bang-singular-bang). To determine when to switch between these modes, we resort to numerical solutions via dynamic programming (DP). One of the subjects is then simulated on four courses, including the Duathlon National Championship in Greenville, SC, USA, in 2019. The DP simulation results show a 24% reduction in travel time over experimental results of the self-paced subject who is a competitive amateur cyclist. This article concludes with a description of a pilot laboratory experiment in which the subject’s trial time was reduced by 3% when the near-optimal pace was communicated to her in real time.