In this work, we investigate the cycle-based optimal NOx emission control for Diesel engine selective catalytic reduction (SCR) systems. The optimization is carried out based on the SCR model and the SCR is assumed to be a continuous stirred tank reactor during the modeling. Considering the main chemical reactions inside an SCR cell, a three-state nonlinear model is obtained and the system parameters are determined by using the experimental data. The states of the nonlinear model consist of the NOx concentration, the ammonia concentration, and the ammonia coverage ratio. Though there are considerable works on the SCR dosing control in the literature, the optimal control strategy applied to the SCR systems has been rarely studied. The global optimality in the SCR dosing control can be used as a benchmark and evaluate the performance of other designed controllers. Moreover, it can be employed to find the limit of NOx conversion efficiency of a specific SCR aftertreatment system and select the minimal volume of the SCR catalyst cell. Therefore, it is quite meaningful to study the optimal NOx emission control of SCR systems via the dynamic programming approach. For the optimization, the challenges arise from the following aspects: (1) Due to the system stiffness, we cannot find an equivalent discrete-time model for the traditional dynamic programming, that is, the traditional dynamic programming algorithm is not applicable. (2) The computational load is relatively too heavy and a personal PC is not affordable. To deal with the existing challenges, we propose the dynamic programming algorithm based on the continuous-time SCR model. The computational load is adjustable in terms of the accuracy. The proposed algorithm is then applied to the SCR system for the NOx emission reduction. And the algorithm validation is carried out based on the US06 test cycle. It infers from the optimization results and the comparison, the prescribed ammonia slip constraint is satisfied and the tailpipe NOx emission is optimized. (C) 2014 Elsevier Ltd. All rights reserved.