Maximisation of stability ranges for recurrent neural networks subject to on-line adaptation
Jochen J. Steil, Helge Joachim Ritter · 1999
. We present conditions for absolute stability of recurrent neural networks with time-varying weights based on the Popov theorem from non-linear feedback system theory. We show how to maximise the stability bounds by deriving a convex optimisation problem subject to linear matrix inequality constraints, which can efficiently be solved by interior point methods with standard software. 1 Introduction One of the most exciting properties of recurrent neural networks (RNN) is their ability to model the time-behaviour of arbitrary dynamical systems [6]. With a number of schemes available which incrementally adapt a network using time-dependent error signals [13] recurrent networks can solve identification and adaptive control tasks in larger systems [8,14]. In such applications the proper functioning of the control system then crucially depends on the the dynamical behaviour of the network. Thus one of the most investigated issues in RNN theory is stability, especially the existence and uni...