NaN problem in MATLAB, LMI, disturbance rejection

[Andrea Weber]

Hi,

can anyone help me? I'm trying to make the disturbance rejection in LMI for my TP model. If I run Matlab, F gain is NaN and I don't know where the problem is:

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

 

Some important informations: 

E = diag([1 2 3 4]);
E = E(:, 1:2);

lmi.F = lmi.F + [1/2*(X*Ar'-M{s}'*Br'+Ar*X-Br*M{s}+X*As'-M{r}'*Bs'+As*X-Bs*M{r})-((1/2*X*(Cr+Cs)')*(eye(lmi.p)^(-1))*1/2*(Cr+Cs)*X)-(1/2*(E)*(((phi^2)*eye(lmi.p))^(-1))*1/2*(Cr+Cs)*X) >= 0];

Thank you!

Andrea

[Johan Löfberg]

As always, supply reproducible code (and tell us which solver you are using)

[Andrea Weber]

Okay, here are the codes and functions:

lmi = lmistructh(Sc, 4);
lmi = lmi_asymhi(lmi,0.23)
F   = lmi_solve(lmi);

function lmi = lmistructh(S, n)

I = size(S);
sizes = I(1:end-2);
R = prod(sizes);

S = reshape(S, [R I(end-1) I(end)]);

m = I(end) - n; 
p = I(end-1) - n; 
A = S(:, 1:n, 1:n);
B = S(:, 1:n, n+1:n+m);
C = S(:, n+1:n+p, 1:n);
D = S(:, n+1:n+p, n+1:n+m);


X = sdpvar(n, n, 'symmetric');
M = cell(1, R);
for r = 1:R
M{r} = sdpvar(m, n, 'full');
end

lmi.F = [X > 0];
lmi.sizes = sizes;
lmi.n = n;
lmi.m = m;
lmi.p = p;
lmi.A = A;
lmi.B = B;
lmi.C = C;
lmi.D = D;
lmi.X = X;
lmi.M = M;

function lmi = lmi_asymhi(lmi,gamma)

R = size(lmi.A, 1);
A = lmi.A;
B = lmi.B;
C = lmi.C;

E = diag([1 2 3 4]);
E = E(:, 1:2);

X = lmi.X;
M = lmi.M;
n = lmi.n;
m = lmi.m;
p = lmi.p;

for r = 1:R
for s = r+1:R
Ar = reshape(A(r,:,:), [n n]);
As = reshape(A(s,:,:), [n n]);
Br = reshape(B(r,:,:), [n m]);
Bs = reshape(B(s,:,:), [n m]);
                Cr = reshape(C(r,:,:), [p n]);
                Cs = reshape(C(s,:,:), [p n]);

 lmi.F = lmi.F + [1/2*(X*Ar'-M{s}'*Br'+Ar*X-Br*M{s}+X*As'-M{r}'*Bs'+As*X-Bs*M{r})-(1/2*X*(Cr+Cs)')*(eye(lmi.p)^(-1))*1/2*(Cr+Cs)*X-1/2*(E)*(((phi^2)*eye(lmi.p))^(-1))*1/2*(Cr+Cs)*X >= 0];

    end
end

function [F P] = lmi_solve(lmi)
%LMI_SOLVE

% solve
solvesdp(lmi.F);
checkset(lmi.F)

P = inv(double(lmi.X));
R = size(lmi.A, 1);
F = zeros(R, lmi.m, lmi.n);
for r = 1:R
F(r,:,:) = double(lmi.M{r}) * P;
end
F = reshape(F, [lmi.sizes lmi.m lmi.n]);

[Johan Löfberg]

To begin with, your code appears to have been written 10-15 years ago since it uses completely obsolete functions such as solvesdp, double and checkset

however, your code is not reproducible as you use local data