A learning algorithm for applying synthesized stable dynamics to system identification

In this paper the models discussed by Cohen are extended by introducing an input term. This allows the resulting models to be utilized for system identification tasks. This approach gives a direct way to encode qualitative information such as attractor dimension into the model. We prove that this model is stable in the sense that a bounded input leads to a bounded state when a minor restriction is imposed on the Lyapunov function. By employing this stability result, we are able to find a learning algorithm which guarantees convergence to a set of parameters for which the error between the model trajectories and the desired trajectories vanishes.