Why is the optimization problem solved by lsqnonlin but not by fmincon ?

Hi All,

Equation 1:

Equation 2:

Equation 1 represents the exact dynamics of a system and equation 2 is the approximate dynamics that will give the same time course profiles as equation 1, upon optimization. For the sake of understanding, let us assume eq(1) gives experimental values and equation 2 are the predicted values.

The objective function defined has a cost function that minimizes the difference between state variables ϕ and , by optimizing parameter which are the control variables.

I've set up this problem using fmincon and lsqnonlin. lsqnonlin gives me the optimal solutions but fmincon doesn't. I am not sure if the problem is with the way I have defined the objective function for fmincon.

I'm attaching the code here. Could someone have a look and help me in sorting out the error?

Here are my results,

lsqnonlin

Dhat =

   1.0e+03 *

    5.0005
    5.0002
    5.0002
    5.0002
    4.9997
    4.9969
    4.9811
    4.8900
    4.9051

fmincon

                                           First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
   61     620    7.524263e-02    0.000e+00    2.745e-05    9.076e+02
   62     630    7.480933e-02    0.000e+00    2.455e-05    1.462e+03
   63     640    7.379937e-02    0.000e+00    2.048e-05    2.348e+03
   64     650    7.166047e-02    0.000e+00    1.810e-05    3.539e+03
   65     660    6.774032e-02    0.000e+00    1.674e-05    4.621e+03
   66     670    6.190134e-02    0.000e+00    1.256e-05    4.315e+03
   67     680    5.473854e-02    0.000e+00    1.030e-05    1.564e+03
   68     690    4.461448e-02    0.000e+00    7.863e-06    4.629e+03
   69     701    2.801994e-02    0.000e+00    4.636e-05    1.486e+04
   
   

After 69th iteration

Matrix dimensions must agree.

Error in cse_03_19_20/objfun (line 37)
    f = (phi - phi_tilde).*(phi - phi_tilde);

Error in barrier

Error in fmincon (line 824)
    [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] = barrier(funfcn,X,A,B,Aeq,Beq,l,u,confcn,options.HessFcn, ...

Error in cse_03_19_20 (line 14)
   Dhat = fmincon(@objfun,Dhat0,[],[],[],[],[],[],[], opts)

chnage to make in attached file: line5

solver = struct('lsq',false); while running fmincon and true while running lsqnonlin