Merging MISO ARX models

Hello guys, how are you doing?

I am trying to mergem multiple MISO ARX models using the merge(m1,..,mN) function, but I am receiving the following error:

Error using idParametric/merge

Models being merged must be of the same type, input-output size and structure.

I was able to merge the iddata, but not the models! Here what I am trying to do:

Estimation Data:

Ze1 = iddata(Ye1, [Ue1, Ue2, Ue3], 1);
Ze2 = iddata(Ye2, [Ue1, Ue2, Ue3], 1);
Ze3 = iddata(Ye3, [Ue1, Ue2, Ue3], 1);

Validation Data:

Zv = iddata(Yv1, [Uv1, Uv2, Uv3], 1);

The idea is to use each estimation data to model each individual input-output and then join the resulting models, as bellow:

Ye1(z) = G11(z)U1(z)
Ye2(z) = G21(z)U2(z)
Ye3(z) = G31(z)U3(z)

Y(z) = Ye1(z)+Ye2(z)+Ye3(z) => 
Y(z) = G11(z)U1(z) + G21(z)U2(z) + G31(z)U3(z)

To make that, I did the following code:

NN = struc(1:30 ,1:30 ,1:30);

N1 = selstruc(arxstruc(Ze1(:,:,1),Zv(:,:,1),NN));
arx1 = arx(Ze1, "na", N1(1), "nb", [N1(2) 0 0], "nk", [N1(3) 1 1]);
 
N2 = selstruc(arxstruc(Ze2(:,:,2),Zv(:,:,2),NN));
arx2 = arx(Ze2, "na", N2(1), "nb", [0 N2(2) 0], "nk", [1 N2(3) 1]);
 
N3 = selstruc(arxstruc(Ze3(:,:,3),Zv(:,:,3),NN));
arx3 = arx(Ze3, "na", N3(1), "nb", [0 0 N3(2)], "nk", [1 1 N3(3)]);

If I then make the merge below,

ARX = merge(arx1, arx2, arx3)

I get the error "Models being merged must be of the same type, input-output size and structure."

If, however, I joing the dataset, no errors are returned.

Ze = merge(Ze1, Ze2, Ze3)

Can anyone help me figure out what is the problem? What I really want is to merge the post-fitted ARX models!

Thanks a lot!

Answer 1

[Rajiv Singh]

What you need is horizontal concatenation, not MERGE which is about statistical merger of identical (same I/Os and model structure) models.

ARX = [arx1, arx2, arx3]