Approximation techniques techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces

We investigate an optimal control problem involving a class of fractional evolution equations in separable Hilbert spaces. The strategy of this paper is establishing low dimensional approximations for this type of equations by using approximation methods. We derive three kinds of convergence results of mild solutions under appropriate assumptions. Then, the convergence result holds for cost functional as well. Further, error estimates of cost functional and optimal controls are obtained. Finally, the proposed concept is supported by an illustrated example. (C) 2018 Elsevier Ltd. All rights reserved.