一类具有等级结构的种群系统的最优控制

Optimal control of a class of population system with hierarchical structure

研究一类基于个体等级差异的种群系统的最优控制问题.首先,利用不动点定理证明了系统解的存在唯一性;其次,利用特征线法和积分不等式证明了解对控制变量的连续依赖性;最后,通过共轭系统和法锥性质得到了最优控制的必要性条件.

The optimal control problem of a class of population system based on individual level difference is studied.Firstly,the existence and uniqueness of solution of the system are obtained by using the fixed point theorem.Then the continuous dependence of the solution on the control variable is proved by means of characteristics and integral estimations.Finally,the necessary conditions of optimal control are obtained by using conjugate system and normal cone.