具有年龄结构和空间扩散种群系统的最优边界控制的逼近解

Approximation of the optimal boundary control for population systems with spatial diffusion

具有空间扩散和年龄结构的种群系统的数学模型和解的性质已有大量的结果,但其边界控制的求解问题比较困难,很有必要给出一种有效的新解法.本文利用辅助原理技巧给出了求解具有年龄结构和空间扩散的种群系统的最优边界控制的迭代算法,并证明了由算法产生的迭代序列的收敛性.

The formulation and the solution character of time-varying population system with age-dependence and spatial diffusion have been studied, but the optimal boundary control is hard to solve, it is necessary to give a new algorithm for the optimal boundary control. The iterative algorithm is constructed for the optimal boundary control of time-varying population system with age-dependence and spatial diffusion by using the auxiliary principle technique. The convergence of iterative sequences generated by the algorithm is also proved.