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This paper will examine the estimation and control of distributed parameter systems which have application to the shape control of a large deployable communications antenna (~100 meters in diameter). Such an antenna would be collapsed and carried into orbit by the NASA space shuttle. Once in orbit, the antenna would automatically deploy like a collapsable umbrella. The antenna surface would be quite flexible and its shape would be adjusted by several attached cords or stringers. After long periods of operation, the antenna surface would require refocusing due to changes in the elastic properties of structure and thermal loads. This fine-tuning would be accomplished by an on-line control system which would process sensor measurements at various locations on the structure to estimate the present antenna shape and then generate control commands to the stringers to bring the antenna back to the desired shape. This is an example of a quasi-static parameter estimation and control problem for a distributed parameter system. Procedures will be developed for synthesis of implementable (finite-dimensional) parameter estimation and control algorithms for this type of problem based on finite element structure analysis.