This study presents a methodology to achieve a desired periodic response in systems with unknown dynamics by optimizing the periodic input. The input and output signals are represented using their Fourier series components, allowing the system behavior to be modeled in the frequency domain. Broyden’s method is employed for the sequential optimization of the input vector to minimize the error in the output response. To reduce the learning time, the system’s dynamic response is accelerated using either passive or active (e.g., feedback control) techniques. Further speedup is achieved through the use of a neural network. The input and output vectors from each optimization iteration are stored and used as the training data for the neural networks, which are trained intermittently. The trained network takes the desired output vector as input and predicts a suitable input vector. This predicted vector serves as the initial guess for Broyden’s method, allowing fine-tuning to improve accuracy without requiring a complex neural network. The effectiveness of the proposed approach is demonstrated on a two-link robotic arm system.