In this paper, we obtain the approximate solutions for optimal control of linear systems, which have a quadratic performance index. The differential transform method (DTM) is applied for solving the extreme conditions obtained from the Pontryagin’s maximum principle. The differential transform method is one of the approximate methods, which can be easily applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Applying DTM, we construct an optimal feedback control law. The results reveal that the proposed method are very effective and simple. Comparisons are made between the results of the proposed methods, homotopy perturbation method, Adomian decomposition method and exact solutions.

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