时变人口发展系统非竞争人口生育率的最优控制

The Optimal Control on the Noncompetitive Fertility Rate for the Time-dependent Population Developing System

讨论了时变人口发展系统的整体解,并且将非竞争人口生育率作为控制函数,用二次泛函来判别其最优性,研究了上述人口系统的控制问题.本文利用L2(Ω)空间的自反性、光滑性和严格凸性,证明了时变人口发展系统最优控制的存在性和唯一性.

We discuss the eotire solution of the time-dependent population developing system equation. We regard the noncompetitive fertility rate as control function and judge its optimality by quadratic functional, and study the optimal control problems for the above population system. Utilizing the reflexivity, smoothness and strict convexity of L^2（Ω） space, we prove the existence and uniqueness of the optimal control for the time-dependent population developing system.