This work presents an interval analysis (IA) based method for the tolerance analysis and robust design of shaped reflector antennas generating contour beams. First, the expression of the power pattern of the contour beam is properly defined in terms of the azimuth and elevation angles and the Cartesian IA (CIA) is then used to derive the lower and upper bounds of the corresponding interval function. The reliability of the proposed CIA tolerance method is analyzed through a set of representative numerical examples including random surface deformations of the reflector surface. Finally, the Particle Swarm Optimizer (PSO) is integrated with the CIA-based interval analysis method for the robust design of shaped reflector antennas. The robustness of the obtained solutions is validated against the results from analytic Monte Carlo simulations and the commercial solver GRASP.

On-orbit space deployable antennas withstand periodic thermal loads, which will degrade the antenna surface accuracy. Thus, it is necessary to preliminarily adjust the antenna before launch to make it adapt to the space temperature environment as much as possible. Aiming at this problem, a pre-adjustment method based on min-max concept is presented in this study. First, according to the force equilibrium equation of the cable element, the incremental equilibrium equation of the cable mesh antenna is derived, and the incremental expressions of the reflector's surface displacement and cable tension with respect to cable length variation and element temperature variation are also developed. Then, the optimization model for shape pre-adjustment is established using min-max method, and the pre-adjustment process is implemented by sequence planning strategy. Finally, an AstroMesh antenna is employed to demonstrate the validity of the method.