Numerical algorithms for solving optimal control problems with integro-differential equations of the second kind as constraints

This study presents numerical algorithms for solving optimal control problems with a class of integro-differential equations of the second kind as costraints. This class of equations consists of an integro-differential term containing an Abeltype kernel. The first kind equations, with a weakly singular kernel, investigated here appear in the mathematical model of an aeroelasticity problem [1]. Two controls are considered in this study: delay and stochastic. The feasibility of the proposed numerical algorithm is demonstrated with examples in which the costs are compared with deterministic optimal controls without time lag.