This work proposes a real-time model predictive control (MPC) system using control Lyapunov-barrier functions (CLBF) and recurrent neural network (RNN) models to ensure simultaneous closed-loop stability and operational safety for a general class of nonlinear systems subject to time-varying disturbances. An RNN model is first developed for the nominal system (i.e., without disturbances) and incorporated in the designs of CLBF-based MPC and of CLEF-based economic MPC (EMPC) to provide state predictions for the optimization problems of MPCs. Subsequently, to improve the closed-loop performance in terms of operational safety and stability in the presence of disturbances, online learning of RNN models is incorporated within the real-time implementation of CLBF-MPC and of CLBF-EMPC to update the RNN models using the most recent process measurement data. The proposed adaptive machine-learning-based CLBF-MPC and CLBF-EMPC schemes are evaluated using a nonlinear chemical process example. (C) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.