NAN matrices #926

nargessC · 2021-06-18T07:38:17Z

nargessC
Jun 18, 2021

Hi, I have written a code and used YALMIP to solve LMI and my aim is that I want to find a fuzzy controller gain matrix. But it results in NAN matrices. It would be a huge help if you can help me find out what's the cause of this problem. My code is as follow and I have attached the paper I'm working on.

A1=[1 0; 2 1];A2=[1 0;2*0.01*pi 1];
B1=[2/2.8 ; 0];B2=[2/2.8 ; 0];
%%
nx=2; epsbar=0.8 ; vi=[0.05;0.45] ; vj=vi ; e=sqrt(epsbar*(1-epsbar))
ZERO=1e-6 ; umax=10
% variables
ro=sdpvar(1); U=sdpvar(nx); H=sdpvar(nx); X1=sdpvar(1,nx); X2=sdpvar(1,nx);
Z1=sdpvar(nx,nx); Z2=sdpvar(nx,nx); xk=[-0.5*pi ; 0]; Q=0.03*eye(nx) ; R=0.001 ; obj=ro
% defined conditions 
cond1=[-1 , xk'; -U , xk];
%
cond2=[(-umax.^2) ,(sqrt(epsbar)*X1.').'  ; (sqrt(epsbar)*X1.') , U - H - H.']
cond22=[(-umax.^2) ,(sqrt(epsbar)*X2.').'  ; (sqrt(epsbar)*X2.') , U - H - H.']
%%
    cond3= [(vi(1)*(U - H.' -H))    , (sqrt(vi(1))*(A1*H+epsbar*B1*X1)).' ,((sqrt(vi(1)))*e*B1*X1).',....
    ((sqrt(vi(1)))*(Q^1/2)*H).'     ,      ((sqrt(vi(1))*epsbar)*X1).'    ,  (sqrt(1-vi(1))*Z1).'   ;.....
    sqrt(vi(1))*(A1*H+epsbar*B1*X1) ,               -U                    ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    (sqrt(vi(1)))*e*B1*X1           ,             zeros(nx)               ,   -U                    ,......
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    (sqrt(vi(1))*(Q^1/2)*H)         ,            zeros(nx)                ,   zeros(nx)             ,......
    -ro*eye(nx)                     ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    sqrt(vi(1)*epsbar)*X1           ,             zeros(1,nx)             ,       zeros(1,nx)       ,.....
    zeros(1,nx)                     ,             -ro*R.'                 ,       zeros(1,nx)       ;.....
    sqrt(1-vi(1))*Z1                ,             zeros(nx)               ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   -ro*eye(nx)           ]
 
 cond33= [(vi(2)*(U - H.' -H))      , (sqrt(vi(2))*(A2*H+epsbar*B2*X2)).' ,((sqrt(vi(2)))*e*B2*X2).',....
    ((sqrt(vi(2)))*(Q^1/2)*H).'     ,      ((sqrt(vi(2))*epsbar)*X2).'    ,  (sqrt(1-vi(2))*Z2).'   ;.....
    sqrt(vi(2))*(A2*H+epsbar*B2*X2) ,               -U                    ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    (sqrt(vi(2)))*e*B2*X2           ,             zeros(nx)               ,   -U                    ,......
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    (sqrt(vi(2))*(Q^1/2)*H)         ,            zeros(nx)                ,   zeros(nx)             ,......
    -ro*eye(nx)                     ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    sqrt(vi(2)*epsbar)*X2           ,             zeros(1,nx)             ,   zeros(1,nx)           ,.....
    zeros(1,nx)                     ,             -ro*R.'                 ,   zeros(1,nx)           ;.....
    sqrt(1-vi(2))*Z2                ,             zeros(nx)               ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   -ro*eye(nx)           ]
%%
s11=[(vi(1)+vj(2))*(U - H - H.')    ,  (sqrt(vj(2))*(A1*H+epsbar*B1*X2)).' ,  (sqrt(vj(2))*e*B1*X2).'  ,.....
    (sqrt(vj(2))*(Q^1/2)*H).'       ,  (sqrt(vj(2)*epsbar)*X2).'           ;.....
    sqrt(vj(2))*(A1*H+epsbar*B1*X2) ,                  -U                  ,   zeros(nx)               ,.....
    zeros(nx)                       ,          zeros(nx,1)                 ;....
    sqrt(vj(2))*e*B1*X2             ,          zeros(nx)                   ,   -U                      ,.....
    zeros(nx)                       ,          zeros(nx,1)                 ;.....
    sqrt(vj(2))*(Q^1/2)*H           ,          zeros(nx)                   ,   zeros(nx)               ,......
    -ro*eye(nx)                     ,          zeros(nx,1)                 ;......
    sqrt(vj(2)*epsbar)*X2           ,          zeros(1,nx)                 ,   zeros(1,nx)             ,......
    zeros(1,nx)                     ,          -ro*R.'                     ]
%
s21= [sqrt(1-vj(2))*Z2              ,          zeros(nx)                   ,   zeros(nx)               ,.....
    zeros(nx)                       ,          zeros(nx,1)                   ;.....
    sqrt(vi(1))*(A2*H+epsbar*B2*X1) ,          zeros(nx)                   ,   zeros(nx)               ,.....
    zeros(nx)                       ,          zeros(nx,1)                   ;.....
    sqrt(vi(1))*e*B2*X1             ,          zeros(nx)                   ,   zeros(nx)               ,.....
    zeros(nx)                       ,          zeros(nx,1)                   ;.....
    sqrt(vi(1))*(Q^1/2)*H           ,          zeros(nx)                   ,   zeros(nx)               ,.....
    zeros(nx)                       ,          zeros(nx,1)                   ;.....
    sqrt(vi(1)*epsbar)*X1           ,          zeros(1,nx)                 ,   zeros(1,nx)             ,.....
    zeros(1,nx)                     ,          zeros(1,1)                    ;.....
    sqrt(1-vi(1))*Z2                ,          zeros(nx)                   ,   zeros(nx)               ,.....
    zeros(nx)                       ,          zeros(nx,1)                   ;].....
            
%
s22=[-ro*eye(nx)  ,  zeros(nx)    , zeros(nx)  ,  zeros(nx)   , zeros(nx,1)  , zeros(nx) ;....
    zeros(nx)     ,         -U    , zeros(nx)  , zeros(nx)    , zeros(nx,1)  , zeros(nx) ;........
    zeros(nx)     ,  zeros(nx)    ,  -U        , zeros(nx)    , zeros(nx,1)  , zeros(nx) ;........
    zeros(nx)     ,  zeros(nx)    , zeros(nx)  , -ro*eye(nx)  , zeros(nx,1)  , zeros(nx) ;.....
    zeros(1,nx)   ,  zeros(1,nx)  , zeros(1,nx), zeros(1,nx)  , -ro*R.'    ,zeros(1,nx);.........
    zeros(nx)     ,  zeros(nx)    , zeros(nx)  , zeros(nx)    , zeros(nx,1)  , -ro*eye(nx)]
%
S1=[s11,s21.']
S2=[s21,s22]   
S=[S1;S2]
cond4=S
%%
% i=1 j=1
    cond5= [(U - H.' -H)            ,        (A1*H+epsbar*B1*X1).'        ,         (e*B1*X1).'     ,....
    ((Q^1/2)*H).'                   ,      (sqrt(epsbar)*X1).'            ,            (Z1).'       ;.....
    (A1*H+epsbar*B1*X1)             ,               -U                    ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    e*B1*X1                         ,             zeros(nx)               ,   -U                    ,......
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    ((Q^1/2)*H)                     ,            zeros(nx)                ,   zeros(nx)             ,......
    -ro*eye(nx)                     ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    sqrt(epsbar)*X1                 ,             zeros(1,nx)             ,       zeros(1,nx)       ,.....
    zeros(1,nx)                     ,             -ro*R.'                 ,       zeros(1,nx)       ;.....
    Z1                              ,             zeros(nx)               ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   -ro*eye(nx)           ]
 % i=1 j=2
    cond55= [(U - H.' -H)           ,        (A1*H+epsbar*B1*X2).'        ,         (e*B1*X2).'     ,....
    ((Q^1/2)*H).'                   ,      (sqrt(epsbar)*X2).'            ,            (Z1).'       ;.....
    (A1*H+epsbar*B1*X2)             ,               -U                    ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    e*B1*X2                         ,             zeros(nx)               ,   -U                    ,......
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    ((Q^1/2)*H)                     ,            zeros(nx)                ,   zeros(nx)             ,......
    -ro*eye(nx)                     ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    sqrt(epsbar)*X2                 ,             zeros(1,nx)             ,       zeros(1,nx)       ,.....
    zeros(1,nx)                     ,             -ro*R.'                 ,       zeros(1,nx)       ;.....
    Z1                              ,             zeros(nx)               ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   -ro*eye(nx)           ]
 % i=2 j=2
    cond555= [(U - H.' -H)           ,        (A2*H+epsbar*B2*X2).'       ,         (e*B2*X2).'     ,....
    ((Q^1/2)*H).'                   ,      (sqrt(epsbar)*X2).'            ,            (Z2).'       ;.....
    (A2*H+epsbar*B2*X2)             ,               -U                    ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    e*B2*X2                         ,             zeros(nx)               ,   -U                    ,......
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    ((Q^1/2)*H)                     ,            zeros(nx)                ,   zeros(nx)             ,......
    -ro*eye(nx)                     ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    sqrt(epsbar)*X2                 ,             zeros(1,nx)             ,       zeros(1,nx)       ,.....
    zeros(1,nx)                     ,             -ro*R.'                 ,       zeros(1,nx)       ;.....
    Z2                              ,             zeros(nx)               ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   -ro*eye(nx)           ]
    
% i=2 j=1
 cond5555= [(U - H.' -H)            ,         (A2*H+epsbar*B2*X1).'       ,         (e*B2*X1).'     ,....
    ((Q^1/2)*H).'                   ,      (sqrt(epsbar)*X1).'            ,            (Z2).'       ;.....
    (A2*H+epsbar*B2*X1)             ,               -U                    ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    e*B2*X1                         ,             zeros(nx)               ,   -U                    ,......
    zeros(nx)                       ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    ((Q^1/2)*H)                     ,            zeros(nx)                ,   zeros(nx)             ,......
    -ro*eye(nx)                     ,             zeros(nx,1)             ,   zeros(nx)             ;.....
    sqrt(epsbar)*X1                 ,             zeros(1,nx)             ,       zeros(1,nx)       ,.....
    zeros(1,nx)                     ,             -ro*R.'                 ,       zeros(1,nx)       ;.....
    Z2                              ,             zeros(nx)               ,   zeros(nx)             ,.....
    zeros(nx)                       ,             zeros(nx,1)             ,   -ro*eye(nx)           ]
    
%%
% F= [U>ZERO];
% F= [F,H>ZERO];
% F= [F,Z1>ZERO];
% F= [F,Z2>ZERO];
% F= [F,X1>ZERO];
% F= [F,X2>ZERO];
% F= [F,ro>ZERO];
F= [cond1<= ZERO];
F= [F,cond2<= ZERO];
F= [F,cond22<= ZERO];
F= [F,cond3<= ZERO];
F= [F,cond33<= ZERO];
F= [F,cond4<= ZERO];
F= [F,cond5<= ZERO];
F= [F,cond55<= ZERO];
F= [F,cond555<= ZERO];
F= [F,cond5555<= ZERO];

%%
ops = sdpsettings('verbose',0,'warning',0,'solver', 'sedumi');
sol = optimize(F,obj,ops); 
sol.problem;
ro_opt=value(ro); 
X1_opt=value(X1) ; X2_opt=value(X2) ; H_opt=value(H)
K1opt=X1_opt*inv(H_opt); K2opt=X2_opt*inv(H_opt);

`
Interval-Type-2-Fuzzy-Model-Predictive-Control-of-Nonlinear-Networked-Control-Systems.pdf

Answered by johanlofberg

Jun 18, 2021

First issues is that you are doing

X <= 1e-6

which is equivalent to

X <= 1e-6*ones(n)

What you intended is

X <= 1e-6*eye(n)

Another issues is that you haven't checked symmetry of the stuff you have created. You have bugs causing some expressions to be non-symmetric, leading to element-wise constraints instead of semidefinite cones

>> F
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|    ID|                     Constraint|   Coefficient range|
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|    #1|    Element-wise inequality 4x1|          1e-06 to 1|
|    #2|          Matrix inequality 3x3|        1e-06 to 100|
|    #3|          Matrix inequality 3x3|        1…

View full answer

johanlofberg · 2021-06-18T07:46:24Z

johanlofberg
Jun 18, 2021
Maintainer

First issues is that you are doing

X <= 1e-6

which is equivalent to

X <= 1e-6*ones(n)

What you intended is

X <= 1e-6*eye(n)

Another issues is that you haven't checked symmetry of the stuff you have created. You have bugs causing some expressions to be non-symmetric, leading to element-wise constraints instead of semidefinite cones

>> F
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|    ID|                     Constraint|   Coefficient range|
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|    #1|    Element-wise inequality 4x1|          1e-06 to 1|
|    #2|          Matrix inequality 3x3|        1e-06 to 100|
|    #3|          Matrix inequality 3x3|        1e-06 to 100|
|    #4|   Element-wise inequality 49x1|          1e-06 to 1|
|    #5|   Element-wise inequality 49x1|          1e-06 to 1|
|    #6|        Matrix inequality 20x20|     1e-06 to 1.3416|
|    #7|        Matrix inequality 11x11|          1e-06 to 2|
|    #8|        Matrix inequality 11x11|          1e-06 to 2|
|    #9|        Matrix inequality 11x11|          1e-06 to 2|
|   #10|        Matrix inequality 11x11|          1e-06 to 2|
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

For instance, the fourth constraint cond3 which isn't symmetric

>> cond3
Linear matrix variable 11x11 (full, real, 12 variables)
Coeffiecient range: 0.001 to 1

...and never turn of solver display until you know everything is running perfectly fine

1 reply

nargessC Jun 18, 2021
Author

thank you so much for your response sir, I will check them.

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NAN matrices #926

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NAN matrices #926

nargessC Jun 18, 2021

Replies: 1 comment · 1 reply

johanlofberg Jun 18, 2021 Maintainer

nargessC Jun 18, 2021 Author

nargessC
Jun 18, 2021

Replies: 1 comment 1 reply

johanlofberg
Jun 18, 2021
Maintainer

nargessC Jun 18, 2021
Author