1. A method of controlling a plant through on-line tuning of a multi-layer neural network, comprising the steps of: obtaining data on output characteristics of the plant; estimating a functional output of the plant from past output of the plant and current values of a plurality of neural network weights and a plurality of neural network layer activation functions; initializing said neural network weights to give an initial neural network output of zero; updating said neural network weights to tune said multi-layer network in accordance with weight tuning equations: EQU W.sub.1 (k+1)=W.sub.1 (k)-.alpha..sub.1 .phi..sub.1 (k)y.sub.1.sup.T (k)-.GAMMA..parallel.I-.alpha..sub.1 .phi..sub.1 (k).phi..sub.1.sup.T (k).parallel.W.sub.1 (k), and EQU W.sub.2 (k+1)=W.sub.2 (k)-.alpha..sub.2 .phi..sub.2 (k)y.sub.2.sup.T (k)-.GAMMA..parallel.I-.alpha..sub.2 .phi..sub.2 (k).phi..sub.2.sup.T (k).parallel.W.sub.2 (k), and in accordance with one of the modified weight update equations: EQU a) W.sub.3 (k+1)=W.sub.3 (k)-.alpha..sub.3 .phi..sub.3 (k)f.sup.-T (k)-.GAMMA..parallel.I-.alpha..sub.3 .phi..sub.3 (k).phi..sub.3.sup.T (k).parallel.W.sub.3 (k), EQU b) W.sub.3 (k+1)=W.sub.3 (k)-.alpha..sub.3 .phi..sub.3 (k)r.sup.T (k)-.GAMMA..parallel.I-.alpha..sub.3 .phi..sub.3 (k).phi..sub.3.sup.T (k).parallel.W.sub.3 (k),; obtaining an error function from past and present output of the plant and a desired output of said plant; determining a response function to control future output of the plant; outputting said response function to the plant; and controlling the plant using said response function.