Optimal control for an age-dependent predator-prey system in a polluted environment

In this paper, we investigate an optimal control problem for an age-dependent predator-prey hybrid system in a polluted environment. Namely, we establish a new toxicant-population model with age-dependence in an environment with small toxicant capacity. By using a 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 the control problem. The existence of optimal control policy is carefully verified by means of Ekeland’s variational principle.