Sedumi 1.3 on YALMIP: Dual infeasible, primal improving direction found

sharmila svsas

unread,

Jan 19, 2018, 5:01:37 AM1/19/18

to YALMIP

clc;

clear all;

global A

global B

global C

global D

global E

global L

global M

global K

yalmip('clear');

c1=1;

C1=[c1 0 0 0;

0 c1 0 0;

0 0 c1 0;

0 0 0 c1];

A{1}=[-.021 0;

0 -2];

A{2}=[-1 -.031;

0 -2];

B=[.021

-1];

D{1}=[-.011

1];

D{2}=[1;

0];

E{1}=[-.022 0;

0 .013];

E{2}=[-.010 0;

0 -.041];

C{1}=[0 .011];

C{2}=[0 0.011];

%%v{2}=C{2}'*C{2};

K{1}=[-.1 -1];

K{2}=[-1.02 -1];

M{1}=1;

M{2}=.91;

zer=[0 0;0 0];

zer1=[0;0];

L=[1.01 0.95];

Omeg1=[1 0 0;0 0 0;0 0 0];

In=[1 0;0 1];

rho=0.03;

alpha=0;

beta=1;

sigma=0.005;

taum=.2;

tauM=1;

n=size(C1,1);

ze=zeros(n,n);

ze1=zeros(4,3);

ze2=zeros(4,1);

ze3=zeros(3,1);

ze4=zeros(3,3);

CR{1}=sigma*alpha*In+(sigma*beta+1)*C{1}'*C{1};

CR{2}=sigma*alpha*In+(sigma*beta+1)*C{2}'*C{2};

for k=1:2

for l=1:2

a{k,l}=[A{k} zer;

zer A{l}+B*K{l}]

end

for l=1:2

a{l}=[-B*M{l}*C{l} zer; zer -B*M{l}*C{l}]

b{l}=[-B*M{l} B*M{l}*C{l}; zer1 zer]

end

for k=1:2

d{k}=[D{k};zer1]

e{k}=[E{k}; zer]

Ome2{k}=[C{k}'; C{k}'];

%Omeg2{k}=Ome2{k}*rho*Omega*Ome2{k}';

dC{k}=[CR{k} CR{k};CR{k} CR{k}]

end

p1=sdpvar(n,n,'symmetric')

p2=sdpvar(n,n,'symmetric')

p3=sdpvar(n,n,'symmetric')

p4=sdpvar(n,n,'symmetric')

p5=sdpvar(n,n,'symmetric')

p6=sdpvar(n,n,'symmetric')

Omega=sdpvar(1,1,'symmetric')

p7=sdpvar(n,n,'symmetric')

%Omega1=sdpvar(3,3,'symmetric')

t=sdpvar(n,n,'full')

gam=sdpvar(1,1,'full')

M11=ze

M22=-p2-p4-p5

M33=-p5+t'+t-p5'

M44=-p3-p5

M55=-Omega*Omeg1

M66=-gam

M77=-1/tauM^2*(p6+p6')

M88=-1/(tauM^2-taum^2)*(p7+p7')

M99=-1/(tauM^2-taum^2)*(p7+p7')-1/tauM^2*(p6+p6')

M1010=-p4

M1111=-p5

M1212=-p6

M1313=-p7

%%%%%%%%%%%%% 1ST ROW

M12=p4

M13=ze

M14=ze

M15=ze1

M16=ze2

M17=1/tauM*(p6+p6')

M18=1/(tauM+taum)*(p7+p7')

M19=1/(tauM)*(p6+p6')+1/(tauM+taum)*(p7+p7')

M110=ze

M111=ze

M112=ze

M113=ze

%%%%%%%%%%%%%% 2ND ROW

M23=p5-t

M24=t

M25=ze1

M26=ze2

M27=ze

M28=ze

M29=ze

M210=ze

M211=ze

M212=ze

M213=ze

%%%%%%%%%%%% 3RD ROW

M34=-t+p5

M35=ze1

M36=ze2

M37=ze

M38=ze

M39=ze

M310=ze

M311=ze

M312=ze

M313=ze

%%%%%%%%%%%% 4TH ROW

%m44=-p3-p5;

M45=ze1

M46=ze2

M47=ze

M48=ze

M49=ze

M410=ze

M411=ze

M412=ze

M413=ze

%%%%%%%%%%%% 5TH ROW

M56=ze3

M57=ze1'

M58=ze1'

M59=ze1'

M510=ze1'

M511=ze1'

M512=ze1'

M513=ze1'

%%%%%%%%%%%% 6TH ROW

M67=ze2'

M68=ze2'

M69=ze2'

M610=ze2'

M611=ze2'

M612=ze2'

M613=ze2'

%%%%%%%%%% 7TH ROW

M78=ze

M79=-1/tauM^2*(p6+p6')

M710=ze

M711=ze

M712=ze

M713=ze

%%%%%%%%%%%% 8th row

M89=-1/(tauM^2-taum^2)*(p7+p7')

M810=ze

M811=ze

M812=ze

M813=ze

%%%%%%%%%%%%% 9TH ROW

M910=ze

M911=ze

M912=ze

M913=ze

%%%%%%%%%%%%%%%%% 10TH ROW

M1011=ze

M1012=ze

M1013=ze

%%%%%%%%%%%%% 11TH ROW

M1112=ze

M1113=ze

%%%%%%%%%%%%% 12TH ROW

M1213=ze

%%%%%%%%%%% 13TH ROW

%2nd matrix

for k=1:2

for l=1:2

m11{k,l}=p1*a{k,l}+a{k,l}'*p1+dC{k}+p2+p3-p4-p6-p6'-(tauM-taum)/(tauM+taum)*(p7+p7')

m110{k,l}=taum*a{k,l}'*p4

m111{k,l}=(tauM-taum)*a{k,l}'*p5

m112{k,l}=tauM/sqrt(2)*a{k,l}'*p6

m113{k,l}=sqrt(tauM^2-taum^2)/sqrt(2)*a{k,l}'*p7

end

m22=ze

m44=ze

m55=ze4

m66=0

m77=ze

m88=ze

m99=ze

m1010=ze

m1111=ze

m1212=ze

m1313=ze

%%%%%%%%%%%%% 1ST ROW

m12=ze;

for l=1:2

m13{l}=p1*a{l}

m15{l}=p1*b{l}

m310{l}=taum*a{l}'*p4

m311{l}=(tauM-taum)*a{l}'*p5

m312{l}=tauM/sqrt(2)*a{l}'*p6

m313{l}=sqrt(tauM^2-taum^2)/sqrt(2)*a{l}'*p7

m510{l}=taum*b{l}'*p4

m511{l}=(tauM-taum)*b{l}'*p5

m512{l}=tauM/sqrt(2)*b{l}'*p6

m513{l}=sqrt(tauM^2-taum^2)/sqrt(2)*b{l}'*p7

end

for k=1:2

m16{k}=p1*d{k}

m610{k}=taum*d{k}'*p4

m611{k}=(tauM-taum)*d{k}'*p5

m612{k}=tauM/sqrt(2)*d{k}'*p6

m613{k}=sqrt(tauM^2-taum^2)/sqrt(2)*d{k}'*p7

m33{k}=Ome2{k}*rho*Omega*Ome2{k}'

end

m14=ze

m17=ze

m18=ze

m19=ze

%%%%%%%%%%%%%% 2ND ROW

m23=ze

m24=ze

m25=ze1

m26=ze2

m27=ze

m28=ze

m29=ze

m210=ze

m211=ze

m212=ze

m213=ze

%%%%%%%%%%%% 3RD ROW

m34=ze

m35=ze1

m36=ze2

m37=ze

m38=ze

m39=ze

%%%%%%%%%%%% 4TH ROW

%m44=-p3-p5;

m45=ze1

m46=ze2

m47=ze

m48=ze

m49=ze

m410=ze

m411=ze

m412=ze

m413=ze

%%%%%%%%%%%% 5TH ROW

m56=ze3

m57=ze1'

m58=ze1'

m59=ze1'

%%%%%%%%%%%% 6TH ROW

m67=ze2'

m68=ze2'

m69=ze2'

%%%%%%%%%% 7TH ROW

m78=ze

m79=ze

m710=ze

m711=ze

m712=ze

m713=ze

%%%%%%%%%%%% 8th row

m89=ze

m810=ze

m811=ze

m812=ze

m813=ze

%%%%%%%%%%%%% 9TH ROW

m910=ze

m911=ze

m912=ze

m913=ze

%%%%%%%%%%%%%%%%% 10TH ROW

m1011=ze

m1012=ze;

m1013=ze

%%%%%%%%%%%%% 11TH ROW

m1112=ze

m1113=ze

%%%%%%%%%%%%% 12TH ROW

m1213=ze

%%%%%%%%%%% 13TH ROW

for k=1:2

for l=1:2

Comi_LMI{k,l}=[m11{k,l} m12 m13{l} m14 m15{l} m16{k} m17 m18 m19 m110{k,l} m111{k,l} m112{k,l} m113{k,l}

m12' m22 m23 m24 m25 m26 m27 m28 m29 m210 m211 m212 m213

m13{l}' m23' m33{k} m34 m35 m36 m37 m38 m39 m310{l} m311{l} m312{l} m313{l}

m14' m24' m34' m44 m45 m46 m47 m48 m49 m410 m411 m412 m413

m15{l}' m25' m35' m45' m55 m56 m57 m58 m59 m510{l} m511{l} m512{l} m513{l}

m16{k}' m26' m36' m46' m56' m66 m67 m68 m69 m610{k} m611{k} m612{k} m613{k}

m17' m27' m37' m47' m57' m67' m77 m78 m79 m710 m711 m712 m713

m18' m28' m38' m48' m58' m68' m78' m88 m89 m810 m811 m812 m813

m19' m29' m39' m49' m59' m69' m79' m89' m99 m910 m911 m912 m913

m110{k,l}' m210' m310{l}' m410' m510{l}' m610{k}' m710' m810' m910' m1010 m1011 m1012 m1013

m111{k,l}' m211' m311{l}' m411' m511{l}' m611{k}' m711' m811' m911' m1011' m1111 m1112 m1113

m112{k,l}' m212' m312{l}' m412' m512{l}' m612{k}' m712' m812' m912' m1012' m1112' m1212 m1213

m113{k,l}' m213' m313{l}' m413' m513{l}' m613{k}' m713' m813' m913' m1013' m1113' m1213' m1313]

end

R=[ M11 M12 M13 M14 M15 M16 M17 M18 M19 M110 M111 M112 M113

M12' M22 M23 M24 M25 M26 M27 M28 M29 M210 M211 M212 M213

M13' M23' M33 M34 M35 M36 M37 M38 M39 M310 M311 M312 M313

M14' M24' M34' M44 M45 M46 M47 M48 M49 M410 M411 M412 M413

M15' M25' M35' M45' M55 M56 M57 M58 M59 M510 M511 M512 M513

M16' M26' M36' M46' M56' M66 M67 M68 M69 M610 M611 M612 M613

M17' M27' M37' M47' M57' M67' M77 M78 M79 M710 M711 M712 M713

M18' M28' M38' M48' M58' M68' M78' M88 M89 M810 M811 M812 M813

M19' M29' M39' M49' M59' M69' M79' M89' M99 M910 M911 M912 M913

M110' M210' M310' M410' M510' M610' M710' M810' M910' M1010 M1011 M1012 M1013

M111' M211' M311' M411' M511' M611' M711' M811' M911' M1011' M1111 M1112 M1113

M112' M212' M312' M412' M512' M612' M712' M812' M912' M1012' M1112' M1212 M1213

M113' M213' M313' M413' M513' M613' M713' M813' M913' M1013' M1113' M1213' M1313]

for k=1:2

for l=1:2

Final_LMI{k,l}=Comi_LMI{k,l}+R

end

ineqs=[Final_LMI{1,1}<0, Final_LMI{1,2}<0, Final_LMI{2,2}<0, p1>0, p2>0, p3>0, p4>0, p5>0, p6>0, p7>0, Omega>0];

opts=sdpsettings;

opts.solver='sedumi';

%ops = sdpsettings('solver','sedumi','sedumi.eps',1e-11);

yalmipdiagnostics=solvesdp(ineqs,[],opts);

yalmipdiagnostics;

gamma=double(sqrt(gam))

Omega=double(Omega)

My problem is with the message I am receiving - " Dual infeasible, primal improving direction found. I have tried to scale the states with a matrix

Johan Löfberg

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Jan 19, 2018, 5:17:01 AM1/19/18

to YALMIP

as always, simplify simplify simplify.

Already the very first constraint you have is infeasible, so you are doomed from the start. Start there...

>> optimize(Final_LMI{1,1}<=0)

ans =

struct with fields:

yalmiptime: 2.2495

solvertime: 1.7085

info: 'Infeasible problem (SDPT3-4)'

problem: 1

sharmila svsas

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Jan 19, 2018, 5:38:23 AM1/19/18

to YALMIP

Ok sir, but whatever I gave values in known matrices, same error appeared. So which type I want to apply values in that known matrices

Johan Löfberg

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Jan 19, 2018, 6:30:23 AM1/19/18

to YALMIP

I have no idea what you are saying.

If you are saying it fails for any dynamical system you try, then it means the theory is wrong, or you have some severe severe bug in your implementation of the problem. We cannot solve that for you

sharmila svsas

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Jan 20, 2018, 12:14:24 AM1/20/18

to YALMIP

I think my doubt is the following steps

Omega=sdpvar(1,1,'symmetric');

Omeg1=[1 0 0;0 0 0;0 0 0];

Omega1=Omega*Omeg1;

.

M55=-Omega1;

.

option1: Is the correct?

option 2: want I define Omega1=sdpvar(3,3,'symmetric');?

option 1 is correct means "Dual infeasible, primal improving direction found"

option 2 is correct means I get a feasibility

Johan Löfberg

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Jan 20, 2018, 3:30:49 AM1/20/18

to YALMIP

sdpvar(1,1,'symmetric') is completely redundant as a scalar always is symmetric (and full).

Dual infeasible means the solver suspects there is no solution to the problem, it is infeasible

Placing the matrix Omega*Omeg1 as a diagonal block in a constraint is very bad. Since Omega1 has zeros on the diagonal, that means you are working with an LMI condition which has zeros in the diagonal, which is numerically ill-conditioned, as that implies that the corresponding rows and columns have to be exactly zero, so the feasible set has no interior. [a b;b 0]>=0 should really be written as a>=0, b==0 for numerical sanity

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