<p>This paper first applies elasticity theory to calculate the torsional deformation of a thin film, and then verifies the accuracy of the deformation results using a finite element method based on solid-shell elements. The Schaaf–Chambre model is employed to derive the torque in a free molecular flow field, thereby establishing a three-axis attitude dynamics model. An RBFNN–SMC approach is adopted to control the three-axis attitude of the atmospheric sail, and its performance is compared with that of SMC alone. The results show that the torques acting on the atmospheric sail are relatively small, all on the order of N·m. The RBFNN can rapidly and efficiently track the nonlinear terms f₁(x), f₃(x) and f₅(x), demonstrating the effectiveness of the RBFNN algorithm. Finally, when the RBFNN–SMC composite control is applied, the required torque M_z of the atmospheric sail is significantly reduced, with a decrease in torque magnitude of up to 55.2%. Moreover, compared with SMC alone, the rotation angles of the sail films (β₂, β₃, β₄) are notably reduced under the composite control. For example, the motor rotation amplitude decreases by 35.6% for the rotation angle β₄. Consequently, the accumulated energy index is lower, indicating that the RBFNN–SMC hybrid control can effectively reduce energy consumption while improving film service life, thereby demonstrating and verifying the superiority of the proposed composite control algorithm.</p>