论文标题

在长距离跑步比赛中最佳控制营养和推进力

Optimally Controlling Nutrition and Propulsion Force in a Long Distance Running Race

论文作者

Cook, Cameron, Lenhart, Suzanne, Hager, William, Chen, Guoxun

论文摘要

参加比赛的跑步者希望优化他们的表现。在本文中,跑步者在种族中的表现,例如马拉松比赛,被称为最佳控制问题,其中控制权是:整个比赛中的营养摄入量和跑步者的推进力量。由于营养是成功运行长距离种族不可或缺的一部分,因此需要将其包括在运行策略的模型中。我们制定了一个普通微分方程的系统,以代表参与长距离种族的跑步者的速度,脂肪能量,糖原能量和营养。能量室代表了跑步者体内可用的能源。我们根据跑步者的移动速度分配跑步者汲取的能源。比赛期间消耗的食物是营养微分方程的来源。借助我们的模型,我们正在研究管理营养和推进力的策略,以最大程度地减少固定距离比赛中的运行时间。这需要解决非平凡的奇异控制问题的解决方案。我们的结果证实了这样一种信念,即举办比赛的最有效方法是在整个比赛中进行大致相同的步伐,而不会让自己的能量达到零。

Runners competing in races are looking to optimize their performance. In this paper, a runner's performance in a race, such as a marathon, is formulated as an optimal control problem where the controls are: the nutrition intake throughout the race and the propulsion force of the runner. As nutrition is an integral part of successfully running long distance races, it needs to be included in models of running strategies. We formulate a system of ordinary differential equations to represent the velocity, fat energy, glycogen energy, and nutrition for a runner competing in a long-distance race. The energy compartments represent the energy sources available in the runner's body. We allocate the energy source from which the runner draws, based on how fast the runner is moving. The food consumed during the race is a source term for the nutrition differential equation. With our model, we are investigating strategies to manage the nutrition and propulsion force in order to minimize the running time in a fixed distance race. This requires the solution of a nontrivial singular control problem. Our results confirm the belief that the most effective way to run a race is to run approximately the same pace the entire race without letting one's energies hit zero.

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