A vast literature has been devoted throughout the years to the construction of both a phase and an amplitude response function that help us study the effects of external stimuli on the dynamics of oscillatory systems. Results trying to reproduce these techniques in the case of damped oscillations have come up recently. Thus, adhering to this recent trend, in this Master's Thesis we complete the study on damped oscillations initiated last year by my colleague Román Moreno in his own Master's Thesis and, based on it, we present a novel optimal control algorithm for the induction of sustained periodic oscillations out of a damped oscillation using a minimum-energy input. The positive results obtained can be seen, from a theoretical point of view, as a deterministic method for the generation of stable structures in systems where they were initially not present; and, from a more practical perspective, they may open the door for therapeutic studies of some neuropathologies when applied to some neuron models in neuroscience.
