This paper proposes numerical methods for addressing optimal control problem; the proposed methods entail using a class of weakly singular integro-differential equations of the second kind as a constraint. The class of weakly singular integro-differential equations of the first kind originates from mathematical models in aeroelasticity. The proposed numerical methods are based on earlier reported approximation schemes for the equations of the first kind. Numerical examples are presented to demonstrate the effectiveness of the proposed methods and the results indicate that the proposed method enables achieving satisfactory and accurate approximations for the targeted systems.

cost functions, optimal controls, optimal states, weakly singular integro-differential equations.