Associative Memory Network Based Modelling of Unknown Nonlinear Systems subject to Immeasurable Disturbances

This paper presents a neural network based scheme for modelling unknown nonlinear systems subject to immeasurable disturbances which satisfy stable, finite-order, recurrence relationships whose parameters are known. The systems considered can be expressed as nonlinear ARMAX models and the disturbance is non-stochastic. Similar to robust servomechanism design, the nonlinear modes of the disturbance are assumed to be known and based upon the knowledge of these modes, a new performance function for modelling the unknown nonlinear function is selected and a gradient descent algorithm which adjusts the weights in the neural network is derived. Convergence of this learning algorithm is proved when the disturbance satisfies a linear recurrence relationship, and the proposed approach is used to model nonlinear time series data which has been corrupted by immeasurable additive sinusoidal noise