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Pseudospectral optimal control is a joint theoretical-computational method for solving optimal control problems. It combines pseudospectral (PS) theory with optimal control theory to produce PS optimal control theory. PS optimal control theory has been used in ground and flight systems in military and industrial applications. The techniques have been extensively used to solve a wide range of problems such as those arising in UAV trajectory generation, missile guidance, control of robotic arms, vibration damping, lunar guidance, magnetic control, swing-up and stabilization of an inverted pendulum, orbit transfers, tether libration control, ascent guidance and quantum control.