Periodic optimal control of ecological systems

The purpose of this paper is to formulate an Optimal control problem which is useful for computing management schemes for ecological systems. Three basic constraints on the problem are considered. The optimal control should maximize a performance measure which reflects a maximization of a selected sum of time-weighted averages of state variables with a sufficient penalty on control. The control should be a positive time function corresponding to an input of material to the system. Finally, the control should be T-periodic in order to be compatible with the cyclic behavior of the ecosystem. Conditions are derived which provide for the existence of controls applicable to ecological problems.