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This paper describes a diesel engine lean NOx trap (LNT) regeneration air to fuel ratio (AFR) control system using a nonlinear model predictive control (NMPC) technique for simultaneous regeneration fuel penalty and overall tailpipe-out NOx reductions. A physics-based and experimentally validated nonlinear LNT dynamic model was employed to construct the NMPC control algorithm, which dictates the AFR value during regenerations. Different choices of NMPC cost function were examined in terms of the impact on fuel penalty and total tailpipe NOx slip amount. The cost function to achieve the best tradeoff between fuel penalty and tailpipe-out NOx was selected based on physical insights into the LNT system NOx and oxygen storage dynamics. The NMPC regeneration AFR control system was evaluated on a vehicle simulator cX-Emissions1 with a 1.9L diesel engine model through the FTP75 driving cycle.