Nl Q Theory: Checking and Imposing Stability of Recurrent Neural Networks for Nonlinear Modelling

It is known that many discrete time recurrent neural networks, such as e.g. neural state space models, multilayer Hoppeld networks and locally recurrent globally feedforward neural networks, can be represented as NL q systems. Suucient conditions for global asymptotic stability and input/output stability of NL q systems are available, including three types of criteria: diagonal scaling and criteria depending on diagonal dominance and condition number factors of certain matrices. In this paper, it is discussed how Narendra's dynamic backpropagation procedure, used for identifying recurrent neural network from I/O measurements, can be modiied with an NL q stability constraint in order to ensure globally asymptotically stable identiied models. An example illustrates how system identiication of an internally stable model, corrupted by process noise, may lead to unwanted limit cycle behaviour and how this problem can be avoided by adding the stability constraint.