problem 5: 'Lack of progress (FMINCON)' using YALMIP. Can someone help me to figure out the problem?

[Ang Zhao]

Hi there,

I am using Matlab R2011b. Here is the program of pole placement. I want to place the poles of the matrix As at p1. 

% pole placement. Set the poles of As to p1.

clear all; clc;

I=eye(3);

O=zeros(3);

% initialization 

k10=sdpvar(1);

a0=sdpvar(1);

b0=sdpvar(1);

c0=sdpvar(1);

d0=sdpvar(1);

% matrices construction

A1=[-k10*I I O;

    O O O;

    O O O;];

B1=[O O;

    I O;

    O I;];

C1=[I O O;

    O O I];

K1=[-d0*1*I -c0*1*I;

    -b0*1*I -a0*1*I];

As=A1-B1*K1*C1;

p0=[-0.04 -0.6 -2]; %

p1=[p0 p0 p0];% expected pole position

A0=diag(p1);

coeffp=poly(As);

coeffp0=poly(A0);

% 

F=[diag(coeffp)-diag(coeffp0)==0];

err = solvesdp(F)

When I ran the code, Matlab generated the following information:

No feasible solution found.

fmincon stopped because the size of the current search direction is less than

twice the default value of the step size tolerance but constraints are not 

satisfied to within the selected value of the constraint tolerance.

<stopping criteria details>

err = 

    yalmiptime: 0.7480

    solvertime: 0.6900

          info: 'Lack of progress (FMINCON)'

       problem: 5

        dimacs: [NaN NaN NaN NaN NaN NaN]

Can someone help me why this happen? 

[Johan Löfberg]

It happens because this is a very hard nonconvex problem, so you will have to rely on luck for anything to work.

Try altering the various options in fmincon, in particular the Algorithm option. When I run it on my machine, it works when I use 'sqp'

[Johan Löfberg]

err = optimize(F,[],sdpsettings('fmincon.algorithm','sqp'))

[Ang Zhao]

Thank you, Mr Johan, however, the code 

err = optimize(F,[],sdpsettings('fmincon.algorithm','sqp'))

does not work on my machine...Matlab shows the following errors:

Undefined function 'optimize' for input arguments of type 'constraint'.

Error in test (line 33)

err = optimize(F,[],sdpsettings('fmincon.algorithm','sqp'))

why is this?

[Johan Löfberg]

You have a very old version of YALMIP and should thus update it.

[Ang Zhao]

It works! Thank you for your consideration!