Optimal control for an age-dependent competitive species model in a polluted environment

In this paper, a new age-dependent toxicant population model in an environment with small toxicant capacity is formulated, and the optimal control problem for this kind hybrid system is investigated. The existence and uniqueness of nonnegative solution of this model is obtained by using a fixed point theorem. The optimality conditions for the control problem are given by means of tangent-normal cone techniques in nonlinear functional analysis. The existence of optimal control policy is carefully verified by using of Ekeland’s variational principle.