1. Class representing neural network nonlinearity estimator for nonlinear ARX models

     net_estimator = neuralnet(Network)

2. Estimate parameters of nonlinear ARX model

    sys = nlarx(Data,Orders,Nonlinearity,Name,Value)

MAtlab methods

 @Joe Rexwinkle

Thank you SIr for your kind reply. My system is a nonlinear model of order 3. It is having one input and another disturbance input (decaying exponential in nature). 

dx1(t)/dt = -p1(x1(t) - Gb) - x1(t) x2(t) + D(t)

dx2(t)/dt = -p2 x2(t) + p3(x3(t) - Ib)

dx3(t)/dt = -p4(x3(t) - Ib) + u(t)

constant parameters: [p1,p2,p3,p4]

state variables: [x1(t), x2(t0, x3(t), x4(t)]

Disturbance: D(t)=Aexp(-Bt)

Input: u(t)

I want to train an ANN whose input to network will be ,

input vector=[model input, model output]

output vector=[p1,p2,p3,p4]

Dear Anirudh,

I think that there is some confusion in your question. In the context of your problem (and in system identification in general) there are two different things: on the one hand there is the model structure (which usually has values that need to be estimated) and on the other there is the estimator (which is an algorithm) used to find estimate for the parameters of the model structure.

Well, a neural network is a model structure, not an estimator. Therefore your question does not make much sense. Two alternative questions that would make sense are: 1) how can I fit (train) a Neural Network to the data from my nonlinear model? The answer to this question would be something like: use a standard estimator such as back propagation. A second question would be: How can I estimate the parameters in my 3D ODE model (from your reply to Joe). The answer to this question would be dependent on the number of measured state variables and etc.

As for your intention to train a NN to produce the parameters at the output, then you want to use an estimator to train the NN to turn it into an estimator of p1 to p4. I agree with Joe, this does not seem the right way of solving this problem. Use some standard estimator. Be aware that what you measure from your system will be crucial to the solution of your problem.

Regards.

Thankyou Sir.