Requirement for shape stability of space structures such as barrel for space telescope tends to become more precisely. In addition to it, large size over 10 meters is sometimes required for such support structure to meet advanced science missions. To realize large and precise support structures, comprehensive techniques including prediction, measurement and stabilization techniques on orbit are needed. In this paper, we introduce some fundamental techniques to keep the precise shape for a slender box truss as a representative support structure. The structural deformation on orbit is induced by thermal distribution, disturbance (RW/MW/SAD etc.) and so on. At first, we analyzed temperature distribution and thermal distortion of the truss structure to predict the thermal deformation. The accuracy of analysis results is evaluated through experiments with a five-bay truss structure. Then, system identification is carried out to identify the stiffness of the structure because such identification of the stiffness becomes important for the precise prediction of thermal deformation in the case of indeterminate structure. As a first step, the stiffness matrix is identified by using particle swarm optimization method from the experimental data of natural frequency. By using the identified stiffness matrix, the natural frequency can be estimated within 1% error. At last, we attempt the shape control of truss structure by using artificial thermal expansion. It is experimentally shown that deformation of truss structure could be controlled with good accuracy, for example, within 30μm error for 1.9m height truss.