Optimal strategy for trail running with nutrition and fatigue factors

This paper presents an extension of Keller's classical model to address the dynamics of long-distance trail running, a sport characterized by varying terrains, changing elevations, and the critical influence of in-race nutrition uptake. The optimization of the generalized Keller's model is achieved through rigorous application of optimal control theory, specifically the Pontryagin Maximum Principle. This theoretical framework allows us to derive optimal control strategies that enhance the runner's performance, taking into account the constraints imposed by the changing terrain, nutritional dynamics, and the evolving fatigue factor. To validate the practical applicability of the model, simulations are performed using real-world data obtained from various mountain races. The scenarios cover various trail conditions and elevation profiles. The performance of the model is systematically evaluated against these scenarios, demonstrating its ability to capture the complexities inherent in long-distance trail running and providing valuable insight into optimal race strategies. The error in the total race-time prediction is of the order of several percent, which may give the runner a reliable tool for choosing an optimal strategy before the actual race.