The integration of shape memory alloys (SMAs) into textile-reinforced composites produces a class of smart materials whose shape can be actively influenced. In this paper, Ni-Ti SMA wires are inserted during the weaving of a glass fiber reinforcement textile. This active reinforcement is then combined with an elastomeric matrix to produce a highly flexible composite sheet, which maintains high rigidity in the longitudinal direction. By activating the SMAs, high deflection ratios of up to 35% (relative to the component's length) are achieved. To adjust the composite's deflection to defined values, a closed-loop control is set up to adjust the current flow through the SMA wires. A control algorithm is designed and evaluated for several test cases. The high deformability and the controllable behavior show the high potential of these materials for applications such as aerodynamic flow control, automation and architecture.