Yalmip LMI solving H2 optimal control problem run into numerical problem

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yuan 2020-7-8

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评论： Paresh yeole 2020-7-9

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Hi, everybody ,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,

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
Kd = 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))
 

any suggestions will be appreciated!

Thanks in advance!