This research introduces a new technique to control constrained nonlinear systems, named Lyapunov-based neural network model predictive control using a metaheuristic optimization approach. This controller utilizes a feedforward neural network model as a prediction model and employs the driving training based optimization algorithm to resolve the related constrained optimization problem. The proposed controller relies on the simplicity and accuracy of the feedforward neural network model and the convergence speed of the driving training based optimization algorithm. The closed-loop stability of the developed controller is ensured by including the Lyapunov function as a constraint in the cost function. The efficiency of the suggested controller is illustrated by controlling the angular speed of three-phase squirrel cage induction motor. The reached results are contrasted to those of other methods, specifically the fuzzy logic controller optimized by teaching learning-based optimization algorithm, the optimized PID with particle swarm optimization algorithm, the neural network model predictive controller based on particle swarm optimization algorithm, and the neural network model predictive controller using driving training based optimization algorithm. This comparative study showcase that the suggested controller provides good accuracy, quickness and robustness due to the obtained values of the mean absolute error, mean square error root mean square error, enhancement percentage, and computing time in the different simulation cases, and it can be efficiently utilized to control constrained nonlinear systems with fast dynamics.