Open Access

ARTICLE

Feasibility of Using Optimal Control Theory and Training-Performance Model to Design Optimal Training Programs for Athletes

Yi Yang, Che-Yu Lin^*

Institute of Applied Mechanics, College of Engineering, National Taiwan University, Taipei City, 106, Taiwan

* Corresponding Author: Che-Yu Lin. Email:

Computer Modeling in Engineering & Sciences 2025, 143(3), 2767-2783. https://doi.org/10.32604/cmes.2025.064459

Received 16 February 2025; Accepted 20 May 2025; Issue published 30 June 2025

Abstract

In order to help athletes optimize their performances in competitions while prevent overtraining and the risk of overuse injuries, it is important to develop science-based strategies for optimally designing training programs. The purpose of the present study is to develop a novel method by the combined use of optimal control theory and a training-performance model for designing optimal training programs, with the hope of helping athletes achieve the best performance exactly on the competition day while properly manage training load during the training course for preventing overtraining. The training-performance model used in the proposed optimal control framework is a conceptual extension of the Banister impulse-response model that describes the dynamics of performance, training load (served as the control variable), fitness (the overall positive effects on performance), and fatigue (the overall negative effects on performance). The objective functional of the proposed optimal control framework is to maximize the fitness and minimize the fatigue on the competition day with the goal of maximizing the performance on the competition day while minimizing the cumulative training load during the training course. The Forward-Backward Sweep Method is used to solve the proposed optimal control framework to obtain the optimal solutions of performance, training load, fitness, and fatigue. The simulation results show that the performance on the competition day is higher while the cumulative training load during the training course is lower with using optimal control theory than those without, successfully showing the feasibility and benefits of using the proposed optimal control framework to design optimal training programs for helping athletes achieve the best performance exactly on the competition day while properly manage training load during the training course for preventing overtraining. The present feasibility study lays the foundation of the combined use of optimal control theory and training-performance models to design personalized optimal training programs in real applications in athletic training and sports science for helping athletes achieve the best performances in competitions while prevent overtraining and the risk of overuse injuries.

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Keywords

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Supplementary Material

Supplementary Material File

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