Abstract: Highlights•A Lyapunov-based predictive control method employs deep learning for nonlinear processes.•A neural ordinary differential equation model learns continuous-time dynamics from data.•Development of the deep neural network control Lyapunov function (DNN-CLF).•Enhancing control performance through Lyapunov-based MPC with DNN-CLF.•Integration of tubes into the MPC scheme for ensured safety.