Techniques for autonomous alignment of beam control systems have been developed for a number of technologies including laser resonators, telescopes, diagnostic systems and components. These techniques have been designed to perform remote autonomous alignment on space based optical systems. An approach building upon these techniques has been developed for autonomous figure control of multi-actuator deformable mirrors. The algorithm used is a multidimensional minimization algorithm based upon the downhill simplex method of Nelder and Mead. This method is well-known for its extreme robustness and its broad applicability to a large variety of problems. In this paper results from numerical studies are presented that demonstrate the ability of this method in performing figure control of a deformable mirror. It is shown that the number of iterations required for the algorithm to converge to a practical solution grows linearly with the number of degrees of freedom. Near optimal numeric solutions are attainable, however, the required number of iterations increases non-linearly.
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