以最佳控制理論研究肌肉持續施力之最佳控制策略

Abstract

在特定的工作和運動中，例如拔河、重訓以及相關勞力工作，大腦下達指令使肌肉進行活動。然而，上述持續施力之活動可能導致肌肉疲勞和相應的肌肉損傷，進而影響工作效率。本論文以肌肉持續施力的數學模型為基礎，探討肌肉在持續施力情境中，施力大小與疲勞程度之關係。在肌肉活動中，施力策略對於減少疲勞和最大程度地提高工作效率極為重要，本研究運用最佳控制理論（Optimal Control Theory）來找尋最佳策略。最佳控制理論為一種數學工具及優化方法，透過解決動態系統的控制問題，以求解出在給定限制條件下的最佳操作策略。 利用最佳控制理論來制定最佳的持續施力策略，以最大程度地減少肌肉疲勞並提高工作效率，使我們肌肉在持續施力情況下，找到大腦控制肌肉的最佳省力模式，以在不引起肌肉過度疲勞的同時實現高效的肌肉活動，故本研究提出了三種施力目標函數，並由數值軟體MATLAB進行量化。這些目標函數考慮大腦施加命令程度、肌肉施力大小及疲勞程度之間關係，並且將此關係結合最佳控制理論，找尋最佳控制策略。同時本研究也將提出之目標函數與未使用最佳控制策略進行分析。藉由上述分析，我們能夠評估不同施力策略的優勢和劣勢，並選擇最有效率的施力方式。

In specific tasks and activities such as tug-of-war, weightlifting, and related physically demanding work, the brain sends commands to the muscles to initiate movement. However, the sustained exertion involved in such activities can lead to muscle fatigue and subsequent muscle damage, ultimately affecting work efficiency. This paper is based on a mathematical model of sustained muscle exertion and explores the relationship between the magnitude of force applied and the level of fatigue experienced. In muscle activities, the strategy of force application plays a crucial role in reducing fatigue and maximizing work efficiency. This study employs Optimal Control Theory to identify the optimal strategy. Optimal Control Theory is a mathematical tool and optimization approach that solves control problems of dynamic systems to determine the best operational strategy under given constraints. Utilizing Optimal Control Theory, this study aims to develop an optimal sustained exertion strategy to minimize muscle fatigue and enhance work efficiency. By considering the optimal energy-saving mode of muscle control by the brain during sustained exertion, we seek to achieve efficient muscle activity without inducing excessive fatigue. To accomplish this, the study proposes three objective functional, quantified using the MATLAB numerical software. These objective functional consider the relationship between the level of commands issued by the brain, the magnitude of muscle force exertion, and the degree of fatigue. By integrating this relationship with Optimal Control Theory, the study seeks to identify the optimal control strategy. Additionally, an analysis comparing the proposed objective functional with the absence of optimal control strategy will be conducted. Through analysis, we can evaluate the advantages and disadvantages of different force strategies and select the optimal approach.