Micromachined membrane deformable mirrors (MMDMs) are commonly utilized in Adaptive Optics (AO) systems due to their relatively good performance and cost-effectiveness. However, these deformable mirrors often exhibit nonlinearity at high control magnitudes and a response that is dependent on external factors such as temperature and humidity. In order to overcome these nonidealities, AO controllers typically implement a linear proportional-integral closed-loop control. Nevertheless, if the model is inaccurate, multiple wavefront (WF) measurements are required, which slow down operations. To address these issues, this thesis proposes a novel approach based on the Direct Inverse Control (DIC) framework, which involves modeling and controlling the AO system using shallow neural networks. Specifically, the specialized learning DIC framework is employed. This approach consists of first identifying a forward model of the plant using a neural network, then placing the controller network in series with the plant one, and finally training the controller to make the overall system resemble an identity transfer function. Since the analyzed system is underdetermined, the controller loss function is augmented with a Lagrangian multiplier. This additional term also enables the regularization of the inversion process, which helps to reduce the risk of saturating actuators. The results of this study show that the proposed approach provides better modeling accuracy
than benchmarks, especially in the working ranges where nonlinearities are present. As a result, it enables faster control convergence than the state-of-the-art method when generating large-phase wavefronts. Moreover, when operating online, the DIC-based method demonstrates better stability and similar tracking abilities to Recursive Least Squares. Overall, the proposed approach provides a promising solution to the challenges associated with using MMDMs in AO systems.