Inflatable, ultra-lightweight antennas using metallized membranes for reflectors are being investigated for use in orbital telescopes and solar energy applications. Simulation results for the control of a simplified model of a membrane using an electric field are reported. The non-linear mapping from position and acceleration of the center of the membrane to control input is learned on-line, and simultaneously used to approximately feedback linearize the SISO plant. Two types of inverse plant model structures are studied: neural nets with sigmoid non-linearities and adaptively constructed look-up tables. In both cases, using only input-output data, the simplified membrane model was successfully stabilized about an unstable equilibrium.