Optimal Control Framework for Individualized Training and Tapering in Swimming

Abstract

Achieving peak performance at a specific competition is a significant challenge in endurance sports like swimming, where balancing training intensity and recovery is key. While tapering, or the strategic reduction of training volume before competition, has been shown to improve performance, current strategies are often heuristic and fail to account for individual variability in physiological response. This thesis addresses the question: How can an individualized training program be designed to balance fitness and fatigue while maximizing performance at a target competition time? Building on the Banister fitness-fatigue model, this research adopts a continuous-time framework to more accurately capture the dynamics of fitness and fatigue. The training optimization problem is formulated as an optimal control problem and solved using the Hamilton-Jacobi-Bellman (HJB) equation. A numerical solver based on the explicit Euler method is used to compute the optimal training intensity over time. Key physiological parameters are individualized using estimates from existing literature, allowing for athlete-specific personalization. Simulation results show that the optimal tapering strategies maintain high fitness while managing fatigue in order to sustain performance. Sensitivity analysis reveals how individual differences in training responsiveness and recovery rates significantly impact the shape and timing of optimal training loads. Athletes with rapid fatigue accumulation, for instance benefit from earlier tapering, while those with better fitness retention can tolerate more aggressive training cycles. This work advances the literature by providing a computational framework that does not merely describe performance trends but actively prescribes individualized training programs. The approach bridges theoretical modeling with practical coaching needs, offering a systematic and data-driven method to design tapering strategies tailored to an athlete’s unique profile.