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In this paper, we present a neurodynamic approach to model predictive control (MPC) of unknown nonlinear dynamical systems based on two recurrent neural networks (RNNs). The echo state network (ESN) and simplified dual network (SDN) are adopted for system identification and dynamic optimization, respectively. First, the unknown nonlinear system is identified based on the ESN with input-output training and testing samples. Then, the resulting nonconvex optimization problem associated with nonlinear MPC is decomposed via Taylor expansion. To estimate the higher order unknown term resulted from the decomposition, an online supervised learning algorithm is developed. Next, the SDN is applied for solving the relaxed convex optimization problem to compute the optimal control actions over the predicted horizon. Simulation results are provided to demonstrate the effectiveness and characteristics of the proposed approach. The proposed RNN-based approach has many desirable properties such as global convergence and low complexity. It is shown that the RNN-based nonlinear MPC scheme is effective and potentially suitable for real-time MPC implementation in many applications.