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This paper presents a fast and global optimization algorithm for an energy-efficient control allocation (CA) scheme, which was proposed for improving the operational energy efficiency of over-actuated systems. For a class of realistic actuator power and efficiency functions, a Karush-Kuhn-Tucker (KKT)-based algorithm was devised to find all the local optimal solutions, and consequently the global minimum through a further simple comparison among all the realistic local minima and boundary values for such a non-convex optimization problem. This KKT-based algorithm is also independent on the selections of initial conditions by transferring the standard nonlinear optimization problem into classical eigenvalue problems. Numerical examples for electric vehicles with in-wheel motors were utilized to validate the effectiveness of the proposed global optimization algorithm. Simulation results, based on the parameters of an electric ground vehicle actuated by in-wheel motors (whose energy efficiencies were experimentally calibrated), showed that the proposed global optimization algorithm was at least 20 times faster than the classical active-set optimization method, while achieving better control allocation results for system energy saving.