一类比例依赖的捕食系统局部能控性及最优控制
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.更多还原Abstract: The locally controllability of positive equilibrium and optimal control problem of a ratio-dependent predator-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 offered to confirm the obtained results. Meanwhile,the optimal control was proved to be of Bang-Bang form by Pontryagin minimum principle.