Large, lightweight telescopes in space will enable future earth science, space science, and reconnaissance. The state of the art in space telescope is the Hubble Space Telescope launched in 1990 with its 2.4 m primary mirror. Missions within the decade such as the Next Generation Space Telescope will push this aperture diameter to over 6.5 m. But truly revolutionary observation in many wavelengths will require increasingly large and lightweight apertures. Although these telescopes of the future will have low areal mass density, the deployed aperture structures must capture and hold a surface figure to a fraction of a wavelength in the presence of thermal, slew, and vibration disturbances. Active control of surface figure is a key technology for the success of gossamer space structures. For structures with thousands of actuators distributed in the surface, the control hardware and computations should be distributed as well. This paper discusses how an efficient control of a membrane reflector shape can be achieved using embedded actuators distributed over the membrane surface. Advanced algorithms using only local information about errors and actuation for collocated and neighboring positions in each of the distributed computational elements allow achieving required control performance. Electrostatic actuators implemented on compliant plastic substrates, represent a highly attractive proposition thanks to their very low areal density. Control, sensing, and communication is distributed and integrated in the adaptive membrane to provide the imaging surface quality of a thick stiff mirror at an infinitesimal fraction of the mass. An adaptive membrane with built-in distributed actuators, sensors, and computational elements can be made scalable to a very large size.