基于尺度结构的非线性竞争种群的最优控制

Optimal control of nonlinear competing populations based on the size-structure

研究了一类基于尺度结构的非线性竞争种群系统的最优控制问题。首先采用特征线法和不动点定理证明了可分离形式解的存在惟一性,然后导出共轭系统,利用切锥-法锥概念给出Bang-Bang型的最优控制和最优控制的必要条件,最后进行了数值模拟。

The optimal control of nonlinear competing population systems based on the size-structure is studied in this paper. Firstly, the existence and uniqueness of separable form solutions are proved by using the method of characteristic lines and the fixed point theorem. Then, the adjoint system is derived. Finally, the optimal control of Bang-Bang type and the necessary condition of optimal control are given by using the concept of tangent and normal cones.