Yalmip LMI solving H2 optimal control problem run into problem

[David peter]

Dear Professor,

 

　 l am trying to use Yalmip toolbox to solve H2 optimal control problem．

l use the following LMI, While there is something wrong with my code, l can't get the expected result,

l use the formula (4.4,4.6,4.7)

clear;

clc;

% system parameters

A = [-3 -2 1;

　1 2　1;

1 -1 -1];

B1 = [1 0.2 0]';

B2 = [0.4 1 0.6]';

C1 = [1.2 0.5 0.3];

D12 = 1;

% declare the variable

P = sdpvar(3);

Z = sdpvar(1);

F = sdpvar(1,3);

mu = sdpvar(1);

% describe the LMI

mat1 = [A*P+P*A'+B2*F+F'*B2' P*C1'+F'*D12';

(P*C1'+F'*D12')' -eye(1)];

mat2 = [Z B1';

B1 P];

% declare the constraints

F = [mat1<0; mat2>0; P>0; Z>0 ;trace(Z)<mu];

optimize(F, mu);

% result

K = value(F)*inv(value(P)）

H2_norm = sqrt(value(mu))

I get the following result ,

SeDuMi 1.3 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.

Alg = 2: xz-corrector, theta = 0.250, beta = 0.500

eqs m = 11, order n = 14, dim = 44, blocks = 4

nnz(A) = 61 + 0, nnz(ADA) = 97, nnz(L) = 54

it : b*y gap delta rate t/tP* t/tD* feas cg cg prec

0 : 2.90E+00 0.000

1 : -6.66E-01 6.49E-01 0.000 0.2239 0.9000 0.9000 1.72 1 1 1.9E+00

2 : -7.69E-01 1.94E-01 0.000 0.2995 0.9000 0.9000 1.17 1 1 5.3E-01

3 : -9.76E-01 6.63E-02 0.000 0.3410 0.9000 0.9000 0.50 1 1 2.2E-01

4 : -1.18E+00 2.25E-02 0.000 0.3396 0.9000 0.9000 0.25 1 1 9.0E-02

5 : -1.44E+00 9.77E-03 0.000 0.4343 0.9000 0.9000 0.10 1 1 6.0E-02

6 : -1.75E+00 3.75E-03 0.000 0.3836 0.9000 0.9000 0.03 1 1 3.7E-02

7 : -2.16E+00 1.33E-03 0.000 0.3553 0.9000 0.9000 0.22 1 1 1.9E-02

8 : -2.46E+00 5.28E-04 0.000 0.3964 0.9000 0.9000 0.23 1 1 1.1E-02

9 : -2.79E+00 1.44E-04 0.000 0.2725 0.9000 0.9000 0.58 1 1 3.6E-03

10 : -2.93E+00 3.91E-05 0.000 0.2716 0.9000 0.9000 0.68 1 1 1.2E-03

11 : -2.99E+00 3.03E-06 0.000 0.0775 0.9900 0.9900 0.90 1 2 9.5E-05

12 : -2.99E+00 1.98E-07 0.000 0.0653 0.9900 0.9900 0.97 1 2 6.3E-06

13 : -2.99E+00 3.82E-08 0.000 0.1934 0.9000 0.9000 0.93 3 3 1.3E-06

14 : -2.99E+00 1.16E-08 0.000 0.3044 0.9000 0.9000 0.76 7 4 4.6E-07

15 : -2.99E+00 4.26E-09 0.000 0.3662 0.9000 0.9000 0.60 16 14 2.1E-07

Run into numerical problems.

iter seconds digits c*x b*y

15 0.1 5.9 -2.9940592991e+00 -2.9940558596e+00

|Ax-b| = 2.8e-07, [Ay-c]_+ = 6.4E-08, |x|= 2.2e+02, |y|= 1.7e+02

Detailed timing (sec)

Pre IPM Post

8.500E-02 1.940E-01 7.800E-02

Max-norms: ||b||=1, ||c|| = 2,

Cholesky |add|=0, |skip| = 0, ||L.L|| = 167.62.

the error message:

错误使用 lmi/value (line 12)

Double not applicable on list of constraints

出错 H2_state_feedback_control_LMI_method (line 274)

Kd = value(F)*inv(value(P))

I have check my code several times ， l don’t know how to deal with this problem,

Any suggestion will be appreciated !

Best Regards

David

[Johan Löfberg]

First, don't you get a lot of sad kittens telling you strict inequalities aren't supported?

As for the question, you are using the variable name F for two different things hence it is no longer an sdpvar when you try to extract value

[David peter]

 Thank  you very much ！！！   it works !   it  was a avoidable mistake. l was too careless

Again  thanks Professor !

clear; clc;

% system parameters

A = [-3 -2 1;

　  1   2　1;

      1 -1 -1];

B1 = [1 0.2 0]';

B2 = [0.4 1 0.6]';

C1 = [1.2 0.5 0.3];

D12 = 1;

% declare the variable

P = sdpvar(3);

Z = sdpvar(1);

F = sdpvar(1,3);

mu = sdpvar(1);

% describe the LMI

mat1 = [A*P+P*A'+B2*F+F'*B2' P*C1'+F'*D12';

               (P*C1'+F'*D12')' -eye(1)];

mat2 = [Z B1';

             B1 P];

% declare the constraints

Fd = [mat1<=0; mat2>=0; P>=0; Z>=0 ;trace(Z)<=mu];

optimize(Fd, mu);

% result

K = value(F)*inv(value(P)）

H2_norm = sqrt(value(mu))