人口预测及带状态约束的最优控制问题

发布时间：2018-11-17 18:41

【摘要】：中文摘要：本文从实际社会人口学的研究问题出发,提出了一类特殊的人口预测问题,即预测未来人口可能达到的最大值与最小值.这类问题可以被描述成带约束条件的最优控制问题.本文首先证明了最优控制的存在性,然后构造出了最优对的形式,并证明了它确实是原问题的最优解.在此基础上,本文又提出了一个终端状态固定的新问题,并得到了类似的结论.最后,利用动态规划的方法重新分析了这一带状态约束的最优控制问题,给出了值函数并讨论了值函数的性质以及它所满足的HJB方程.
[Abstract]:Abstract: this paper presents a special population forecasting problem based on the study of actual social demography, that is, the maximum and minimum values that the population may reach in the future. This kind of problem can be described as an optimal control problem with constraints. In this paper, we first prove the existence of optimal control, then construct the form of optimal pair, and prove that it is the optimal solution of the original problem. On this basis, a new problem of terminal state fixation is proposed and a similar conclusion is obtained. Finally, the optimal control problem with state constraints is reanalyzed by using the dynamic programming method. The value function is given and the properties of the value function and the HJB equation which it satisfies are discussed.
【学位授予单位】：复旦大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O232;C924.2

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