How to use RBF training to simulate this function, (simulation and using code seperatly)

f = @(x)(prod([x(1),x(2),x(3),x(5),x(3)-1])+x(4)) ./ (1 + x(2)^2 + x(3)^3);

k = 5; % demo value y = 1:5; % demo value u = 1:5; % demo value

y(k+1) = f([y(k), y(k-1), y(k-2), u(k), u(k-1)])

Answer 1

[Leepakshi]

Hi Jabbar,

You can simulate this function using Radial Basis Function Training using below three steps:

1. Simulate the system using your nonlinear function to generate input-output data.
2. Train an RBF network on this data: "newrb" function can help, refer to below example code.
3. Test the RBF network and compare its output to the true function.

Refer to this code for better understanding:

f = @(x)(prod([x(1),x(2),x(3),x(5),x(3)-1])+x(4)) ./ (1 + x(2)^2 + x(3)^3);

N = 200; % .... Generate data using loop and randn, if not available.

X = [y(3:N+2)', y(2:N+1)', y(1:N)', u(3:N+2)', u(2:N+1)']; % Prepare inputs (X) and targets (T)
T = y(4:N+3)';

net = newrb(X', T', 1e-3, 1.0, 50); % Train RBF network

Hope this helps!

Thanks