ABSTRACT Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.

中文翻译：

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异质种群定性研究中的广义函数

摘要 非光滑函数空间的解，包括广义函数和测度，经常出现在最优控制理论中，但在应用中被避免。然而，它们有助于在改进技术的情况下找到对新旧资本设备的最佳投资分配。相应的经济问题涉及年龄结构人口的线性 Lotka-McKendrik 模型中的最优控制。普通函数类中不存在最优解，因此使用广义函数来构造解。资本和投资的最佳年龄分布包括狄拉克函数，并被解释为对特定年龄设备的瞬时投资。数值模拟完成了动力学的呈现。