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This paper presents a novel technique adaptive shape control of a parabolic space antenna with the help of an optimized SMA-wire network. The work uses genetic algorithm NSGA-II for solution of the problem, which has minimization of energy input and minimization of error in desired and obtained shape as the two conflicting objectives. We combine finite element analysis with well-established temperature-resistance models of SMA wire and use them to obtain the optimal network of SMA wire along with the actuation temperature for each wire in the network.

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