融合空间扩散与等级结构的种群系统的最优收获控制

何泽荣, 秦婉玉

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (2) : 240-254.

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PDF(435 KB)
系统科学与数学 ›› 2022, Vol. 42 ›› Issue (2) : 240-254. DOI: 10.12341/jssms21347

融合空间扩散与等级结构的种群系统的最优收获控制

    何泽荣, 秦婉玉
作者信息 +

Optimal Harvesting Control of Hierarchical Population Systems with Diffusion

    HE Zerong, QIN Wanyu
Author information +
文章历史 +

摘要

分析一类基于个体等级差异和空间扩散的种群模型的最优收获控制问题,系统演化模型由二阶偏微分积分方程表征.运用Aubin引理和极值化序列方法建立了最优解的存在性,借助法锥理论和共轭系统技巧给出了最优控制器的特征刻画.所获成果为实际应用奠定基础.

Abstract

This article analyzes a class of optimal harvesting control problems. The evolution of the population is modeled by a second-order integro-partial differential equation. Applying Aubin's lemma and an extremalizing sequence, we establish the existence of optimal solutions. The characteristic description of optimal strategies is derived by means of theory of normal cones and the technique of adjoint systems. The results lay a solid foundation for applications.

关键词

扩散 / 年龄等级 / 最优控制 / 紧嵌入 / 法锥

Key words

Dispersion / hierarchy of ages / optimal control / compact imbedding / normal cone

引用本文

导出引用
何泽荣 , 秦婉玉. 融合空间扩散与等级结构的种群系统的最优收获控制. 系统科学与数学, 2022, 42(2): 240-254. https://doi.org/10.12341/jssms21347
HE Zerong , QIN Wanyu. Optimal Harvesting Control of Hierarchical Population Systems with Diffusion. Journal of Systems Science and Mathematical Sciences, 2022, 42(2): 240-254 https://doi.org/10.12341/jssms21347
中图分类号: 92B05    49K20    49J20   

参考文献

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基金

国家自然科学基金(11871185)资助课题.
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