摘要
考虑一类具年龄等级结构的n维食物链种群系统的最优收获问题,首先利用压缩映射定理,研究系统解的适定性;其次构造极值化序列和运用相关的紧性定理证明控制问题最优解的存在性;最后通过构造共轭系统和利用法锥的概念刻画,得出最优收获问题最优解的一阶必要条件.
Optimal harvest problem of an n-dimensional food chain population system with hierarchical age-structure is considered.Firstly,the existence uniqueness of the system solution is studied by using the principle of compression mapping.Secondly,the existence of the optimal solution of the control problem is proved by using extremum sequences and the compactness theorem.Finally,by constructing appropriate conjugate systems and utilizing the concept of the cone,the first-order necessary conditions for the optimal solution of the optimal harvesting problem are obtained.
作者
贺亚权
雒志学
HE Yaquan;LUO Zhixue(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《应用数学》
北大核心
2024年第1期133-147,共15页
Mathematica Applicata
基金
国家自然科学基金(11561041)
甘肃省自然科学基金(1506RJZA071)。
关键词
年龄等级
最优控制
食物链
共轭方程组
Hierarchy of ages
Optimal control
Food chain
System of conjugate equations