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An efficient computational method is presented for the synthesis of singular optimal control in this paper. The proposed numerical procedure consists of two phases: initialization and refinement. In the initialization phase, the original singular optimal contrl (SOC) problem is converted into nonsingular one by adding to the performance index a perturbed (or weighted) energy term. The resultant boundary value problem can easily be solved for an appropriately large value of the perturbation parameter. In the refinement phase, the solution obtained from the initialization phase is refined in a systematic manner based on continuation methods until the optimal (or sub-optimal) solution to the original SOC problem is achieved. One of the major advantages of the proposed algorithm is that the resultant two-point boundary value problem needs to be solved just one time and the refinement of the solution is accomplished by solving a set of initial value problems sequentially and/or in parallel as the perturbation parameter goes to zero. The proposed algorithm is, therefore, computationally efficient and applicable to a large class of optimal control problems with various boundary conditions (e.g., fixed and free terminal time). The practicability of the method is demonstrated by computer simulations on several example problems.