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This brief presents nonlinear control strategies for a single quadrant unity power factor rectifier. First, a standard average model is utilized to design an adaptive controller and exponential stability of the controlled system is demonstrated via a Lyapunov stability argument. It is shown that: (1) the initial output voltage needs to be sufficiently large to ensure boundedness of the system in closed loop and (2) there is an upperbound on the rate of adaptation to guarantee system stability in the closed loop. It is shown that unmodeled non-idealities in the system lead to sub-par controller performance at low loads. To account for these, an improved system model is presented that accounts for the non-idealities by a constant disturbance matched with the control input. This is followed by a redesign of the controller to make it adaptive to such a disturbance. Finally, experimental results with the redesigned controller showing significantly enhanced performance at low load are presented.