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Nonlinear Model predictive control (NMPC) suffers from the problems of closed loop instability and computational complexity, which greatly limit the applications of NMPC in real plants involving fast time-varying dynamics. During previous work, the authors have supposed a new real-time NMPC algorithm based on the concept of generalized pointwise min-norm (GPMN) scheme. And in this paper, the new real-time NMPC is generalized to deal with the nonlinear systems with control input constraints. The main contribution of this paper is to find out the analytic form of GPMN controller for input constrained nonlinear systems, and then parameterize it to formulate the real time NMPC controller - called - GPMN-enhanced NMPC (GPMN-ENMPC). Finally, in the last section, the simulations with respect to the mobile robot with orthogonal wheel are conducted to verify the feasibility and validity of the new given algorithm.