In this talk, we introduce Semi-Autonomous Neural Ordinary Differential Equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. Specifically, with respect to their classical counterpart, SA-NODEs are characterized by time-independent parameters, making them suitable not only for simulation, but also for prediction. We begin by investigating the universal approximation properties of SA-NODEs for dynamical systems from both a theoretical and a numerical perspective. Within the assumption of a finite-time horizon, under general hypotheses we establish an asymptotic approximation result, demonstrating that the error vanishes as the number of parameters goes to infinity. Under additional regularity assumptions, we further specify this convergence rate in relation to the number of parameters, utilizing quantitative approximation results in the Barron space. The time-independence of the hyperparameters makes SA-NODEs suitable for prediction, in situations where the underlying physical system is unknown. Following the theoretical discussion in the first part of the talk, we will present some current investigations concerning the application of SA-NODEs to Model Predictive Control. Our numerical experiments validate the effectiveness of SA-NODEs in capturing the dynamics of various ODE systems and transport equations. Additionally, we compare SA-NODEs with vanilla NODEs, highlighting the superior performance and reduced complexity of our approach.