| 基于尺度结构的非线性竞争种群的最优控制 |
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| 引用本文： | 郑秀娟,雒志学,张昊.基于尺度结构的非线性竞争种群的最优控制[J].山东大学学报(理学版),2021,56(11):51-60. |
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| 作者姓名： | 郑秀娟 雒志学 张昊 |
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| 作者单位： | 兰州交通大学数理学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金资助项目(11561041) |
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| 摘 要： | 研究了一类基于尺度结构的非线性竞争种群系统的最优控制问题。首先采用特征线法和不动点定理证明了可分离形式解的存在惟一性,然后导出共轭系统,利用切锥-法锥概念给出Bang-Bang型的最优控制和最优控制的必要条件,最后进行了数值模拟。
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| 关 键 词： | 尺度结构 竞争种群 共轭系统 最优控制 |
Optimal control of nonlinear competing populations based on the size-structure |
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| ZHENG Xiu-juan,LUO Zhi-xue,ZHANG Hao.Optimal control of nonlinear competing populations based on the size-structure[J].Journal of Shandong University,2021,56(11):51-60. |
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| Authors: | ZHENG Xiu-juan LUO Zhi-xue ZHANG Hao |
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| Institution: | School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China |
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| Abstract: | The optimal control of nonlinear competing population systems based on the size-structure is studied in this paper. Firstly, the existence and uniqueness of separable form solutions are proved by using the method of characteristic lines and the fixed point theorem. Then, the adjoint system is derived. Finally, the optimal control of Bang-Bang type and the necessary condition of optimal control are given by using the concept of tangent and normal cones. |
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| Keywords: | size-structure competitive population adjoint system optimal control |
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