Necessary and sufficient conditions for near-optimal harvesting control problem of stochastic age-dependent system

In this paper, we consider a near-optimal harvesting control problems for stochastic age-structured population system. We establish necessary and sufficient conditions for near-optimality. These conditions are described by adjoint equations and a nearly maximum condition on the Hamiltonian. The proof of the main result is based on Ekeland's variational principle and the adjoint processes with respect to the control variable. As is well known, optimal controls may fail to exist even in simple cases. This justifies the use of near-optimal controls, which exist under minimal assumptions and are sufficient in most practical cases. At last, an example is given for illustrating our results.