"The coefficient matrix is not full row rank, numerical problems may occur. "" and " Infeasible problem (SeDuMi-1.3) "
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Vu Thanh
Nov 17, 2020, 6:14:57 AM11/17/20
to YALMIP
%%
clc
clear
close all
%% Define the parameter
J1 = 1.69;
C1 = 0.01;
K1 = 6652;
J2 = 0.01;
C2 = 0.02;
K2 = 2561;
J3 = 0.09;
C3 = 7.82;
K3 = 50.4;
C4 = 5.31;
K4 = 215;
Kt = 3.56;
Ke = 3.32;
R = 0.21;
%% Define the matrices
A = [ 0 1 0 0 0 0 0;
-(K1)/J1 (-(C1/J1)+((Kt*Ke)/(J1*R))) K1/J1 C1/J1 0 0 0;
0 0 0 1 0 0 0;
K1/J2 C1/J2 -(K1+K2+K4)/J2 -(C1+C2+C4)/J2 K2/J2 C2/J2 0;
0 0 0 0 0 1 0;
0 0 K2/J3 C2/J3 (-K2-K3)/J3 -C2/J3 K3/J3;
0 0 0 0 K3/C3 0 -K3/C3];
B = [ 0; -Kt/(J1*R); 0; 0; 0; 0; 0 ];
%% Output
%C =eye(7);% [ 0 0 1 0 0 0 0];
C1 = [ 1 0 0 0 0 0 0;
0 1 0 0 0 0 0;
0 0 1 0 0 0 0;
0 0 0 1 0 0 0;
0 0 0 0 1 0 0;
0 0 0 0 0 1 0;
0 0 0 0 0 0 1];
%C2 =[0; 0; 1; 0; 0; 0; 0];
D2 = zeros(7,1);
%% figure
p1 = eig(A)
p = 1.0e+02 * [-2.6409 + 9.3842i ; -2.6409 - 9.3842i ; -0.0553 + 1.4895i ; -0.0553 - 1.4895i ; -0.0298 + 0.0000i ; -0.0843 + 0.0000i ; -0.2933 + 0.0000i ];
K = - place(A,B,p) %関数”place”ではBのランクを超える固有値の重複は許されない。
eig(A+B*K)
sim('test2model');
figure
plot(t,x(:,3));
ylabel('blade_angel');
xlim([0 2]);
saveas(gcf,'blade_angel.png');
figure
plot(t,x(:,4));
ylabel('blade_dot');
xlim([0 1]);
saveas(gcf,'blade_dot.png');
%% LMI可解問題
n = length(A); %n:x(t)の次元
alpha = 2; %alpha=2
ep = 1e-6; %十分小さな正数 = 10^(-6)
P = sdpvar(n,n,'sy');
LMI = [P >= ep*eye(n)];
LMI2 = LMI + [A'*P + P*A +2*alpha*P <= -ep*eye(n)];
solvesdp(LMI2) %LMI可解問題の求解
P2 = double(P) %実行能解 P を表示
And Result
The coefficient matrix is not full row rank, numerical problems may occur.
SeDuMi 1.3.4 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, theta = 0.250, beta = 0.500
eqs m = 28, order n = 22, dim = 148, blocks = 4
nnz(A) = 190 + 0, nnz(ADA) = 784, nnz(L) = 406
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 6.46E+11 0.000
1 : 0.00E+00 1.33E+11 0.000 0.2052 0.9000 0.9000 1.00 1 1 7.7E+05
2 : 0.00E+00 2.56E+10 0.000 0.1928 0.9000 0.9000 1.00 1 1 1.5E+05
3 : 0.00E+00 5.01E+09 0.000 0.1960 0.9000 0.9000 1.00 1 1 2.9E+04
4 : 0.00E+00 1.57E+08 0.000 0.0313 0.9900 0.9900 1.00 1 1 9.2E+02
5 : 0.00E+00 3.20E+07 0.000 0.2035 0.9000 0.9000 0.88 1 1 2.1E+02
6 : 0.00E+00 2.40E+06 0.000 0.0751 0.9900 0.9900 0.50 1 1 2.6E+01
7 : 0.00E+00 4.83E+05 0.000 0.2014 0.9000 0.9000 -0.70 1 1 2.7E+01
8 : 0.00E+00 3.02E+04 0.000 0.0625 0.9900 0.9900 -0.96 1 1 2.9E+01
9 : 0.00E+00 8.19E+02 0.000 0.0271 0.9900 0.9900 -1.00 1 1 2.9E+01
10 : 0.00E+00 2.16E+01 0.000 0.0264 0.9900 0.9900 -1.00 1 1 2.9E+01
11 : 0.00E+00 5.69E-01 0.000 0.0264 0.9900 0.9900 -1.00 2 2 2.9E+01
12 : 0.00E+00 1.50E-02 0.000 0.0264 0.9900 0.9900 -1.00 2 2 2.9E+01
13 : 0.00E+00 3.85E-04 0.000 0.0257 0.9900 0.9900 -1.00 2 2 2.9E+01
14 : 0.00E+00 1.16E-04 0.000 0.3006 0.9000 0.9000 -1.00 2 3 2.9E+01
15 : 0.00E+00 2.27E-05 0.000 0.1965 0.9000 0.9000 -1.00 3 3 2.4E+01
Run into numerical problems.
iter seconds |Ax| [Ay]_+ |x| |y|
15 0.1 4.8e-08 3.0e-17 6.0e+00 5.0e-17
Failed: no sensible solution/direction found.
Detailed timing (sec)
Pre IPM Post
2.002E-03 5.899E-02 1.006E-03
Max-norms: ||b||=0, ||c|| = 1.000000e-06,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 45.7594.
ans =
フィールドをもつ struct:
yalmipversion: '20200930'
matlabversion: '9.4.0.813654 (R2018a)'
yalmiptime: 0.1846
solvertime: 0.0624
info: 'Infeasible problem (SeDuMi-1.3)'
problem: 1
P2 =
1.0e-16 *
-0.1911 -0.0329 0.0184 0.0670 0.0223 0.0604 0.0076
-0.0329 0.0239 -0.0547 0.0001 -0.0475 0.0011 0.0243
0.0184 -0.0547 -0.2224 -0.0928 0.0027 0.0090 0.0057
0.0670 0.0001 -0.0928 -0.0001 0.0229 0.0000 0.0002
0.0223 -0.0475 0.0027 0.0229 -0.2217 -0.0799 0.0052
0.0604 0.0011 0.0090 0.0000 -0.0799 0.0000 0.0031
0.0076 0.0243 0.0057 0.0002 0.0052 0.0031 -0.2902
Johan Löfberg
Nov 17, 2020, 6:28:38 AM11/17/20
to YALMIP
First, there is no official command called solvesdp
The problem you pose is simply not feasible, as SeDuMi tells you. This is trivial to see
For A'*P + P*A + 2*alpha*P <= 0 to hold, with positive alpha and positive definite P, it must hold that
A'*P + P*A < 0 . That condition is equivalent with A being stable, which it isn''t
>> eig(A)
ans =
1.0e+02 *
-2.6402 + 9.3835i
-2.6402 - 9.3835i
-0.0103 + 1.4868i
-0.0103 - 1.4868i
0.2299 + 0.0000i
0.0554 + 0.0000i
-0.0580 + 0.0000i
Message has been deleted
Vu Thanh
Nov 17, 2020, 8:44:41 AM11/17/20
to YALMIP
Thank you for your response.
I have a mistake in A matrix , and i fixed it . Then , i run code again , and i got unwanted result
%%
clc
clear
close all
%% Define the parameter
J1 = 1.69;
C1 = 0.01;
K1 = 6652;
J2 = 0.01;
C2 = 0.02;
K2 = 2561;
J3 = 0.09;
C3 = 7.82;
K3 = 50.4;
C4 = 5.31;
K4 = 215;
Kt = 3.56;
Ke = 3.32;
R = 0.21;
%% Define the matrices
A = [ 0 1 0 0 0 0 0;
-(K1)/J1 ((C1/J1)-((Kt*Ke)/(J1*R))) K1/J1 C1/J1 0 0 0;
================================================================================
and Result
The coefficient matrix is not full row rank, numerical problems may occur.
SeDuMi 1.3.4 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, theta = 0.250, beta = 0.500
eqs m = 28, order n = 22, dim = 148, blocks = 4
nnz(A) = 190 + 0, nnz(ADA) = 784, nnz(L) = 406
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 6.46E+11 0.000
1 : 0.00E+00 1.42E+11 0.000 0.2192 0.9000 0.9000 1.00 1 1 8.3E+05
2 : 0.00E+00 3.15E+10 0.000 0.2225 0.9000 0.9000 1.00 1 1 1.8E+05
3 : 0.00E+00 6.09E+09 0.000 0.1931 0.9000 0.9000 1.00 1 1 3.6E+04
4 : 0.00E+00 2.32E+08 0.000 0.0381 0.9900 0.9900 1.00 1 1 1.4E+03
5 : 0.00E+00 4.27E+07 0.000 0.1840 0.9000 0.9000 0.92 1 1 2.7E+02
6 : 0.00E+00 2.84E+06 0.000 0.0665 0.9900 0.9900 0.60 1 1 2.7E+01
7 : 0.00E+00 5.91E+05 0.000 0.2082 0.9000 0.9000 -0.65 1 1 2.6E+01
8 : 0.00E+00 3.76E+04 0.000 0.0636 0.9900 0.9900 -0.95 1 1 2.9E+01
9 : 0.00E+00 1.17E+03 0.000 0.0312 0.9900 0.9900 -1.00 1 1 2.9E+01
10 : 0.00E+00 3.64E+01 0.000 0.0311 0.9900 0.9900 -1.00 1 1 2.9E+01
11 : 0.00E+00 1.10E+00 0.000 0.0301 0.9900 0.9900 -1.00 1 2 2.9E+01
12 : 0.00E+00 3.40E-02 0.000 0.0310 0.9900 0.9900 -1.00 2 2 2.9E+01
13 : 0.00E+00 1.06E-03 0.000 0.0312 0.9900 0.9900 -1.00 2 2 2.9E+01
14 : 0.00E+00 5.58E-05 0.000 0.0525 0.9900 0.9900 -1.00 2 3 3.1E+01
15 : 0.00E+00 3.24E-05 0.000 0.5804 0.9000 0.9000 -1.00 3 3 3.0E+01
16 : 0.00E+00 2.13E-05 0.000 0.6587 0.9000 0.9000 -1.00 3 3 3.0E+01
Run into numerical problems.
iter seconds |Ax| [Ay]_+ |x| |y|
16 0.1 5.1e-08 1.9e-17 6.1e+00 3.2e-17
Failed: no sensible solution/direction found.
Detailed timing (sec)
Pre IPM Post
2.997E-03 6.100E-02 0.000E+00
Max-norms: ||b||=0, ||c|| = 1.000000e-06,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 71.3251.
ans =
フィールドをもつ struct:
yalmipversion: '20200930'
matlabversion: '9.4.0.813654 (R2018a)'
yalmiptime: 0.3520
solvertime: 0.0640
info: 'Infeasible problem (SeDuMi-1.3)'
problem: 1
P2 =
1.0e-16 *
-0.1414 -0.0360 0.0044 0.0384 0.0158 0.0416 0.0003
-0.0360 -0.0329 -0.0495 -0.0002 -0.0413 -0.0016 0.0040
0.0044 -0.0495 -0.1260 -0.0531 0.0102 0.0081 0.0003
0.0384 -0.0002 -0.0531 -0.0000 0.0127 -0.0000 0.0001
0.0158 -0.0413 0.0102 0.0127 -0.1388 -0.0587 0.0015
0.0416 -0.0016 0.0081 -0.0000 -0.0587 -0.0001 0.0015
0.0003 0.0040 0.0003 0.0001 0.0015 0.0015 -0.1774
2020年11月17日火曜日 20:28:38 UTC+9 Johan Löfberg:
Johan Löfberg
Nov 17, 2020, 1:11:36 PM11/17/20
to YALMIP
You have a classical case of bad formatting with spaces in matlab
>> [A'*P + P*A +2*alpha*P <= -ep*eye(n)]
++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| ID| Constraint| Coefficient range|
++++++++++++++++++++++++++++++++++++++++++++++++++++++++
| #1| Matrix inequality 7x7| 0.0059172 to 1885600|
| #2| Matrix inequality 7x7| 1e-06 to 4|
++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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