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A novel real-time receding horizon tracking control (RHC) strategy is presented for nonlinear discrete-time systems with quadratic criteria for fast controller response. The control law is derived by using the receding horizon concept from the optimal tracking problem. First, the original problem is reduced to an equivalent optimal regulator problem for an offline system by augmenting the state variables and then the optimal control input sequences are successfully derived by a so-called successive approximation approach (SAA) based on vector iteration. An optimal tracking law is obtained by a feasible iterative process. Only the compensate term need to be calculated online in order to reduce the computation costs. Simulations are conducted to demonstrate the feasibility and optimality of the control law obtained.