<p style='text-indent:20px;'>Student engagement in learning a prescribed body of knowledge can be modeled using optimal control theory, with a scalar state variable representing mastery, or self-perceived mastery, of the material and control representing the instantaneous cognitive effort devoted to the learning task. The relevant costs include emotional and external penalties for incomplete mastery, reduced availability of cognitive resources for other activities, and psychological stresses related to engagement with the learning task. Application of Pontryagin's maximum principle to some simple models of engagement yields solutions of the synthesis problem mimicking familiar behaviors including avoidance, procrastination, and increasing commitment in response to increasing mastery.</p>

中文翻译：

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使用最优控制理论模拟学生参与

<p style='text-indent:20px;'>学生参与学习规定的知识体系可以使用最优控制理论建模，标量状态变量代表对材料的掌握或自我感知掌握，对材料的掌握和控制代表用于学习任务的瞬时认知努力。相关成本包括对不完全掌握的情感和外部惩罚、其他活动的认知资源可用性降低以及与参与学习任务相关的心理压力。将 Pontryagin 的最大原理应用于一些简单的参与模型，可以模拟熟悉的行为，包括回避、拖延和随着掌握程度的提高而增加承诺，从而解决综合问题。</p>