運用最佳控制理論及訓練表現模型設計運動員之最適訓練計畫

Abstract

本研究提出一種新的方式，以最佳控制理論結合訓練-表現模型，設計個人化的最佳訓練計畫，目的在幫助運動員在競賽日達到最佳表現，同時預防過度訓練與使用傷害的可能。研究裡採用的訓練-表現模型為 Banister Impulse-Response model的概念延伸，能夠描述訓練負荷（控制變數）、體能（正向影響）、疲勞（負向影響）與表現之間的動態關係。 研究所設計的目標函數，旨在透過提升體能與減少疲勞，以在比賽當日最大化表現，同時在整個訓練期間內盡量減少總訓練負荷。為求解此最佳控制問題，本研究透過前向-後向掃描法（Forward-Backward Sweep Method），已獲得訓練負荷、體能、疲勞與表現等變數隨時間之最佳變化。結果指出，與沒有最佳控制相比，以最佳控制理論可有效降低總訓練負荷並提升比賽日的表現。此外，透過起停式控制 (Bang-Bang control)，訓練負荷可在保持一段期間內恆定，僅於特定時間點進行切換，讓訓練計畫更符合實務操作，更提升效率與最終表現。 本研究奠定了結合訓練-表現模型與最佳控制理論在運動科學領域之基礎，證實其可行性與潛力。未來可導入更符合實際生理現象的非線性模型，以實驗驗證，來建立能真正協助運動員規劃訓練、提升表現並預防過度訓練的科學化系統。

To support athletes in reaching peak performance on competition day meanwhile reducing the risk of overtraining and overuse injuries, this study introduces a novel method that combines optimal control theory with a training-performance model to develop individualized, optimal training programs. The performance model utilized in this work is an extended version of the Banister Impulse-Response model, capturing the dynamic interactions between training load, fitness (representing positive adaptation), fatigue (representing negative effects), and overall performance. The aim of the developed framework for optimal control is to maximize performance at the time of competition by increasing fitness and reducing fatigue, while concurrently minimizing the total training load throughout the training period. The Forward-Backward Sweep Method is employed to address the optimal control problem, yielding time-dependent trajectories of training load, fatigue, fitness, and performance. Simulation outcomes indicate that incorporating optimal control leads to improved competition-day performance with a lower cumulative training load compared to non-optimized approaches. Additionally, the implementation of bang-bang control strategies, where training loads are held constant over specific intervals, offers practical benefits, enhancing both training efficiency and final performance outcomes. This study lays the foundation for applying optimal control theory in sports science, providing a systematic method for developing personalized training programs tailored to individual physiological characteristics. Future work should incorporate more physiologically realistic, nonlinear performance models and validate the proposed method with experimental data to advance toward practical and science-based training optimization for athletes.