The incorporation of advanced control algorithms into prosthetic hands significantly enhances their ability to replicate the intricate motions of a human hand. This work introduces a model-based controller that combines an Artificial Neural Network (ANN) approach with a Sliding Mode Controller (SMC) designed for a tendon-driven soft continuum wrist integrated into a prosthetic hand known as "PRISMA HAND II". Our research focuses on developing a controller that provides a fast dynamic response with reduced computational effort during wrist motions. The proposed controller consists of an ANN for computing bending angles together with an SMC to regulate tendon forces. Kinematic and dynamic models of the wrist are formulated using the Piece-wise Constant Curvature (PCC) hypothesis. The performance of the proposed controller is compared with other control strategies developed for the same wrist. Simulation studies and experimental validations of the fabricated wrist using the controller are included in the paper.