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Abstract: This paper presents an optimal control strategy suitable for investigating the mission performance of a spacecraft equipped with a NASAʼs Evolutionary Xenon Thruster. Using an accurate mathematical model of the propulsion system, based on both experimental data and a semi-empirical schematization of the power generation system, the minimum-time rendezvous problem with various celestial bodies is investigated through an indirect approach. Unlike a conventional approach, in which the thruster power is varied with continuity within a given range, here the solar electric propulsion system is described using a finite number of operation points, characterized by different pairs of thruster input power and propellant mass flow rate. The model includes the possibility of obtaining coasting phases along the spacecraft trajectory. The optimal control strategy is found for a three-dimensional problem in which the actual shape and relative orientation of the initial and final orbits are taken into account. The paper presents the simulation results for a number of minimum-time trajectories towards inner planets (Mercury, Venus, and Mars) and three Near Earth Asteroids (NEAs) of particular interest for the scientific community: 1998 KY-26, 99942 Apophis, and 2007 VK-184. [Copyright &y& Elsevier]