摘要
研究一类具有离散时滞和年龄结构的生物种群模型的最优收获策略,其状态方程由一阶偏泛函微分方程描述.运用极值化序列方法和Mazur定理证明了最优控制的存在性,借助非线性泛函分析中的切锥-法锥和共轭系统技巧导出了最优性条件.通过对共轭系统的细致分析,确立了最优控制的唯一性,给出了最优解的特征刻画.
An optimal harvesting problem is considered for a class of population models with discrete delay and continuous age distribution, whose state system is described by a partial functional differential equation. The existence of optimal strategy is proved by means of maximizing sequence and Mazur＇s theorem, and the first-order optimality conditions are derived out via normal cone and adjoint system techniques. Finally by a detailed analysis for the adjoint system, the uniqueness and the characteristic representation of the optimal controller are given.
出处
《系统科学与数学》
CSCD
北大核心
2010年第1期53-59,共7页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(10771048)资助课题
