CALCULATION OF THE VOLTERRA KERNELS OF NONLINEAR DYNAMIC-SYSTEMS USING AN ARTIFICIAL NEURAL-NETWORK

The Volterra series is a well-known method of describing non-linear dy namic 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-line ar dynamic systems. In this paper we show how a certain class of artif icial neural networks are equivalent to Volterra series and give the e quation for the nth order Volterra kernel in terms of the internal par ameters of the network. The technique is then illustrated using a spec ific non-linear system. The kernels obtained by the method described i n the paper are compared with those obtained by a Toeplitz matrix inve rsion technique.