Optimal control for age-dependent population hybrid system in a polluted environment

In this paper, we study an optimal control problem for an age-dependent population hybrid system in a polluted environment. Namely, we establish a new toxicant-population model with age-dependence in a small content of the environment. By fixed point theorem, we obtain the existence and uniqueness of nonnegative solution of the toxicant-population model with age-dependence. We employ tangent-normal cone techniques in nonlinear functional analysis to deduct the optimality conditions for control problem. The existence of optimal control policy is carefully verified by means of Ekeland’s variational principle.