Calculation of the Volterra kernels of non-linear dynamic systems using an artificial neural network

The Volterra series is a well-known method of describing non-linear dynamic systems. A major limitation of this technique is the difficulty involved in the calculation of the kernels. More recently, artificial neural networks have been used to produce black box models of non-linear dynamic systems. In this paper we show how a certain class of artificial neural networks are equivalent to Volterra series and give the equation for the nth order Volterra kernel in terms of the internal parameters of the network. The technique is then illustrated using a specific non-linear system. The kernels obtained by the method described in the paper are compared with those obtained by a Toeplitz matrix inversion technique. Received: 4 June 1993/Accepted in revised form: 2 March 1994