Recurrent Learning of Input-output Stable Behaviour in Function Space: a Case Study with the Roessler Attractor

We analyse the stability of the input-output behaviour of a recurrent network. It is trained to implement an operator implicitly given by the chaotic dynamics of the Roessler attractor. Two of the attractors coordinate functions are used as network input and the third defines the reference output. Using recently developed new methods we show that the trained network is input-output stable and compute its input-output gain. Further we define a stable region in weight space in which weights can freely vary without affecting the input-output stability. We show that this region is large enough to allow stability preserving on-line adaptation which enables the network to cope with parameter drift in the referenced attractor dynamics.