This article proposes a new and efficient iterative procedure to solve a class of discrete-time nonlinear optimal control problems. Based on the Pontryagin's maximum principle, the necessary optimality conditions are formulated in the form of a nonlinear discrete boundary value problem (BVP). This problem is then reduced into a sequence of linear discrete BVPs by applying a series expansion approach called the modal series method. Solving the aforementioned sequence by using the techniques of

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... lving linear difference equations, the optimal control law is derived in the form of a uniformly convergent series. In order to demonstrate the efficiency of the proposed method in practice, an iterative algorithm with a fast rate of convergence is provided. In a recursive manner, only a few iterations are needed to find a suboptimal control law with enough accuracy. The effectiveness of this new technique is verified by solving some numerical examples.