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Nonlinear model predictive control (NLMPC) is now a widely accepted control technology in many industrial applications. Since the quality of the model of a physical non-linear process plays a critical role in the successful development, deployment, and maintenance of a NLMPC application, the mathematical representation of such models has been the subject of significant research in both academia and industry. In this paper, extrapolating gain-constrained neural networks (EGCN) is described as a key component of a NLMPC technology that has been in use in more than 100 industrial applications over the past 7 years. Simulation results are presented which compare EGCN models to traditional neural network training methods as well as to the recently proposed bounded-derivative network (BDN). These results highlight the critical advantages of EGCN in nonlinear process modeling for optimization and control applications and underscore the effectiveness of EGCN models in providing guarantees on global gain-bounds without compromising accurate representation of available process data.