Abstract:The differential transform method used for solving the approximation analytic solution of the unconstrained optimal control problem is established. According to the state equation, costate equation and governing equation in the set of Hamilton regular equations, we first construct the differential transform form based on initial value or terminal station, by which the optimality condition is transformed into a corresponding algebraic equation, furthermore, the approximation analytic solution of the optimal control problem is obtained. In addition, to the nonlinear optimal control problem which is complex in structure, in particular condition, the discreteness set of algebraic equations can be constructed in light of the principle of approximation by interpolation and the differential transform method to obtain its approximation analytic solution. By using this method, the initial-boundary value problem of the differential equation and the complex system of the functional optimization problems are converted into algebraic equations which facilitate getting the solution, also are simple, feasible and easy to realize. Finally, the effectiveness of this method is verified by numerical examples.