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This paper formulates optimal pacing of a cyclist on hilly terraintime-trials as a minimum-time optimal control problem. Maximal power of acyclist serves as a time-varying constraint and depends on fatigue and recoverywhich are captured via dynamic models proposed early in the paper. Experimentalprotocols for identifying the individualized parameters of the proposed fatigueand recovery models are detailed and results for six human subjects are shown.In an analytical treatment via necessary conditions of Pontryagin MinimumPrinciple, we show that the cyclist's optimal power in a time-trial is limitedto only four modes of all-out, coasting, pedaling at a critical power, orconstant speed (bang-singular-bang). To determine when to switch between thesemodes, we resort to numerical solution via dynamic programming. One of thesubjects is then simulated on four courses including the 2019 Duathlon NationalChampionship in Greenville, SC. The dynamic programming simulation results show24% reduction in travel time over experimental results of the self-pacedsubject who is a competitive amateur cyclist. The paper concludes withdescription of a pilot lab experiment in which the subject trial time wasreduced by 3% when the near-optimal pace was communicated to her in real-time.

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