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A robust model predictive control (MPC) method is proposed for nonlinear affine systems with bounded disturbances. The robust MPC technique requires on-line solution of a minimax optimal control problem. The minimax strategy means that worst-case performance with respect to uncertainties is optimized. The minimax optimization problem involved in robust MPC is reformulated to a minimization problem and then is solved by using a two-layer recurrent neural network. Simulation examples are included to illustrate the effectiveness of the proposed method.