It is often desired to reduce sound radiated from cylindrical shells. Active structural acoustic control (ASAC) provides a means of controlling the structural vibration in a manner to efficiently reduce the radiated sound. Previous work has often required a large number of error sensors to reduce the radiated sound power, and the control performance has been sensitive to the location of error sensors. The ultimate objective is to provide global sound power reduction using a minimal number of local error measurements, while also minimizing any dependence on error sensor locations. Recently, a control metric referred to as weighted sum of spatial gradients (WSSG) was developed for ASAC. Specific features associated with WSSG make this method robust under a variety of conditions. In this work, the WSSG control metric is extended to curved structures, specifically a simply supported cylindrical shell. It is shown that global attenuation of the radiated sound power is possible using only one local error measurement. It is shown that the WSSG control metric provides a solution approximating the optimal solution of attenuating the radiated sound power, with minimal dependence on the error sensor location. Numerical and experimental results are presented to demonstrate the effectiveness of the method.