Design of simple limit cycles with recurrent neural networks for oscillatory control

This work deals with the search of parameters value for recurrent neural networks to generalte a simple default limit cycle, to be used, and shaped for specific cases of oscillatory controller instead of learning to a recurrent neural network to produce the specific oscillator behavior directly. We describe in detail, a generalized form of the "teacher forcing" gradient based algorithm, that can be used in the usual way but also as partial teacher forcing when target signals are not all available. We discuss the drawbacks of the resulting algorithm and propose a modified version in the 2 dimensions case, giving criterions toward higher order cases.