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The performance of a glider can be considerably improved by means of soaring and optimization of its trajectory. Recent advances in the area of static soaring assume known linear glider dynamics and no actuator saturation phenomena. In practice, the dynamics of the glider change with flight and environmental conditions, and the actuators moving the control surfaces have mechanical limits. In this paper, we consider the optimization-based static soaring problem in the presence of actuator saturation nonlinearities and large parametric uncertainties in the dynamics of the vehicle. We use ideas from robust adaptive control and anti-windup design tools to develop an adaptive control scheme based on linear quadratic control with disturbance rejection. The saturation-type nonlinearity is addressed by the proposed adaptive version of a linear matrix inequality based anti-windup design. The resulting adaptive control scheme with adaptive anti-windup augmentation allows optimal soaring despite the presence of significant actuator saturation limits and unknown parameters.