Abstract
This paper generalizes a class of controllability problems based on the scale structure population system model. Based on the comparison principle of linear systems, the solution of the nonlinear system model is obtained by referring to the fixed point theorem. The non-negative, boundedness, existence, and uniqueness of the solution of the system model are established. The optimality condition is described in detail by means of a normal cone and conjugate system under the condition of proving the continuous dependence of the state environment on the solution to control variables.