How to interpolation between matrices

Imagine the plot attached below. Each point on this plot represents a a 4x4 matrix that describes the behavior of the plant at that particular point. For a controller design, I have a reference load which I need to track at a given speed (omega).

How do I interpolate to get the specific 4-D matrix at a load point and speed which is not already a point on the plot?

Thanks!

Answer 1

[Stephen23]

Assuming that you want to interpolate between the corresponding elements of those 4x4 matrices, then you could do something like this:

C = {randi(9,4,4), randi(9,4,4), randi(9,4,4)}; % 4x4 matrices in a cell array
C{:}

ans = 4×4

2 8 7 7 7 1 5 7 7 8 5 5 3 3 2 7

ans = 4×4

1 3 7 1 3 1 5 6 4 3 9 7 9 4 2 5

ans = 4×4

5 3 4 5 2 3 9 3 7 9 6 2 2 3 9 6

L = [1;3;2]; % load
W = [7;8;9]; % omega
M = cat(3,C{:});
[X,Y] = meshgrid(1:numel(C),1:16);
F = scatteredInterpolant(Y(:),L(X(:)),W(X(:)),M(:),'linear','linear');

Interpolate the entire matrix:

Lq = 1.5;
Wq = 7.5;
out = reshape(F({1:16,Lq,Wq}),4,4)

out = 4×4

2.3333 6.3333 6.5000 5.6667 5.5000 1.3333 5.6667 6.1667 6.5000 7.3333 5.8333 4.8333 3.8333 3.1667 3.1667 6.5000

Lq = 2;
Wq = 8;
out = reshape(F({1:16,Lq,Wq}),4,4)

out = 4×4

2.6667 4.6667 6.0000 4.3333 4.0000 1.6667 6.3333 5.3333 6.0000 6.6667 6.6667 4.6667 4.6667 3.3333 4.3333 6.0000

[Prince Essemiah]

Thank you for your detailed answer. One question though, is the '3' in the concatenated line from having three matrices in C? In other words, what would that number be if my cell array C contains 20 matrices?

M = cat(3,C{:});

[Stephen23]

"is the '3' in the concatenated line from having three matrices in C?"

No, it means that we concatenate those matrices along the third dimension.

"In other words, what would that number be if my cell array C contains 20 matrices?"

3