Stochastic optimal control of predator-prey ecosystem by using stochastic maximum principle
Stochastic optimal control of predator-prey ecosystem by using stochastic maximum principle
复制标题
利用随机极大值原理的捕食-被捕食生态系统随机最优控制
DOI：
10.1007/s11071-016-2752-y
复制
发表时间：
2016-07-01
影响因子：
5.6
通讯作者：
Zhu, W. Q.
中科院分区：
文献类型：
--
作者：
Gu, X. D.;Zhu, W. Q.
提出了一种新的防止随机环境中捕食-食饵生态系统灭绝的控制策略。首先，引入受控随机Lotka-Volterra系统，并给出它的一些性质。应用随机平均法将原被控系统转化为部分平均系统。然后，基于随机最大值原理导出了部分平均控制问题的伴随方程和最大值条件。最优控制由最大值条件和求解正倒向随机微分方程确定。对于无限时间区间遍历控制，伴随过程是平稳的，FBBNN被减少到一个常微分方程。最后，得到了最优控制系统的食饵平稳概率密度，表明受控生态系统比不受控生态系统更稳定。最优控制系统的平均过渡时间也计算表明，所提出的控制策略是有效的，在防止可能的灭绝。
A new control strategy for preventing the extinction of predator-prey ecosystem in a random environment is proposed. First, a controlled stochastic Lotka-Volterra system is introduced and its some properties are presented. The stochastic averaging method is applied to transfer the original controlled system to a partially averaged one. Then, the adjoint equation and maximum condition of the partially averaged control problem are derived based on the stochastic maximum principle. The optimal control is determined from the maximum condition and solving the forward-backward stochastic differential equation (FBSDE). For infinite time-interval ergodic control, the adjoint process is stationary and the FBSDE is reduced to an ordinary differential equation. Finally, the stationary probability density of the prey of optimally controlled system is obtained to show that the controlled ecosystem is more stable than the uncontrolled one. The mean transition time of optimally controlled system is also calculated to show that the proposed control strategy is effective in preventing the possible extinction.