Optimal control for a class of nonlinear age-distributed population systems

This paper deals with an optimal control problem for a kind of age-dependent biological population systems. The well-posedness of the state system is treated by means of characteristics line and fixed-point principle. Necessary optimality conditions are obtained via tangent–normal cone technique in nonlinear functional analysis. The existence and uniqueness of the optimal controller are established by the use of Ekeland’s principle.