Space-based astronomy and remote sensing systems would benefit from extremely large aperture mirrors that can permit greater-resolution images. To be cost effective and practical, such optical systems must be lightweight and capable of deployment from highly compacted stowed configurations. Such gossamer mirror structures are likely to be very flexible and therefore present challenges in achieving and maintaining the required optically precise shape. Active control based on dielectric elastomers was evaluated in order to address these challenges. Dielectric elastomers offer potential advantages over other candidate actuation technologies including high elastic strain, low power dissipation, tolerance of the space environment, and ease of commercial fabrication into large sheets. The basic functional element of dielectric elastomer actuation is a thin polymer film coated on both sides by a compliant electrode material. When voltage is applied between electrodes, a compressive force squeezes the film, causing it to expand in area. We have explored both material survivability issues and candidate designs of adaptive structures that incorporate dielectric elastomer actuation. Experimental testing has shown the operation of silicone-based actuator layers over a temperature range of -100 °C to 260 °C, suitable for most earth orbits. Analytical (finite element) and experimental methods suggested that dielectric elastomers can produce the necessary shape change when laminated to the back of a flexible mirror or incorporated into an inflatable mirror. Interferometric measurements verified the ability to effect controllable shape changes less than the wavelength of light. In an alternative design, discrete polymer actuators were shown to be able to control the position of a rigid mirror segment with a sensitivity of 1800 nm/V, suggesting that sub-wavelength position control is feasible. While initial results are promising, numerous technical challenges remain to be addressed, including the development of shape control algorithms, the fabrication of optically smooth reflective coatings, consideration of dynamic effects such as vibration, methods of addressing large-numbers of active areas, and stowability and deployment schemes.