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一类比例依赖的捕食系统局部能控性及最优控制 被引量：3

Locally Controllability and Optimal Control of a Ratio-dependent Predator-prey System
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摘要 研究了一类比例依赖的捕食模型正平衡态的局部能控性及最优控制问题.通过分析的方法并借助Kalman秩条件得到了该模型正平衡态局部能控的充分条件,并用具体的例子进一步验证了结论的正确性.同时证明了相应的最优控制问题最优对的存在性,并利用庞德里亚金最小值原理证明了最优控制必为Bang-Bang控制. The locally controllability of positive equilibrium and optimal control problem of a ratio-dependent pred- ator-prey system were investigated. Based on analysis techniques and Kalman rank condition, the sufficient conditions for locally controllability of the positive equilibrium of the model were obtained. Besides, a specific example was of- fered to confirm the obtained results. Meanwhile, the optimal control was proved to be of Bang-Bang form by Pontryagin minimum principle.
作者 向会立 王刚
机构地区 湖北民族学院数学系 河南城建学院数理学院
出处 《信阳师范学院学报（自然科学版）》 CAS 北大核心 2015年第2期160-162,共3页 Journal of Xinyang Normal University(Natural Science Edition)
基金 国家自然科学基金项目(11261017) 教育部科学技术研究重点项目(212111)
关键词 捕食系统 局部能控性 充分条件 最优控制存在性 BANG-BANG控制 predator-prey system locally controllability sufficient conditions existence of optimal control Bang-Bang control
分类号 O231.2 [理学—运筹学与控制论] O232 [理学—运筹学与控制论]
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参考文献7

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共引文献5

同被引文献28

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引证文献3

信阳师范学院学报（自然科学版）
2015年 第2期

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