In this paper, we give an analytical approximate solution for non-linear quadratic optimal control problems and optimal control of linear systems using the homotopy perturbation method (HPM). Applying the HPM, the non-linear two-point boundary-value problem (TPBVP) and linear systems, derived from the Pontryagin’s maximum principle, are transformed into a sequence of linear time-invariant TPBVPs. Solving the proposed linear TPBVP sequence in a recursive manner leads to the optimal control law and the optimal trajectory in the form of rapid convergent series. Finally, a non-linear example and several linear examples are given to verify the reliability and efficiency of the proposed method.

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