APPLICATION OF FAST AUTOMATIC DIFFERENTIATION FOR OPTIMIZATION OF SYSTEMS OF INTEGRO-DIFFERENTIAL EQUATIONS

Abstract

In this paper, the authorы solve the optimal control problem in the predator-prey model described by a system of Volterra integro-differential equations. The maximum principle for the initial continuous problem is formulated considering the defined constraints and functional form. The initial continuous problem is reduced to the discrete optimal control problem. For the discrete optimal control problem formulas for calculating the gradient of the target function using the method of direct differentiation and the method of fast automatic differentiation are received. The numerical method is developed to construct an approximate optimal solution on the basis of fast automatic differentiation method. It is shown that the obtained numerical results of the approximate optimal control correspond to the maximum principle for the initial continuous problem with a prescribed accuracy.