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Optimization of system ODE

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Nicholas Moung
Nicholas Moung on 21 Jan 2021
Commented: Nicholas Moung on 1 Feb 2021 at 18:29
Hello Matlabers!
I'm using fsolve function for optimization of system of ODE. And I'm facing difficulty now. Could someone advise me with this please? I'm just beginner in using Matlab and I do appreciate your advise.
The functions file is expressed below.
------------------------------------------------------
function fval= SimFnc(X)
%Initial values
dt=1/32;
g=9.8065;
t=1:2003; %number of points
%Importing data from STAT
STAT=importdata('STAT.txt');
nx= STAT(:,10);
ny= STAT(:,11);
nz= STAT(:,12);
Wx_d= STAT(:,7);
Wx_r=deg2rad(Wx_d);
% Wx = interp1(Wx_r,t);
Wy_d= STAT(:,8);
Wy_r=deg2rad(Wy_d);
% Wy = interp1(Wy_r,t);
Wz_d= STAT(:,9);
Wz_r=deg2rad(Wz_d);
Theda_iz=STAT(:,13);
Gamma_iz=STAT(:,14);
Theda_izr=deg2rad(Theda_iz);
Gamma_izr=deg2rad(Gamma_iz);
Alpha_iz=STAT(:,29);
Alpha_izr=deg2rad(Alpha_iz);
Beta_iz=STAT(:,30);
Beta_izr=deg2rad(Beta_iz);
V_iz =STAT(:,28);
%Initial values of Variables
Alpha(1)=0.1587/57.2958;
Beta(1)=0.0143/57.2958;
V(1)=58.0154;
Theda(1)=0.0025/57.2958;
Gamma(1)=0.0013/57.2958;
Erx=X(1);
Ery=X(2);
Erz=X(3);
Erv=X(4);
Erw=X(5);
%Calculating by Euler's method
for i=1:2002
ax=g*(nx(i)-sin(Theda(i)));
ay=g*(ny(i)-cos(Theda(i))*cos(Gamma(i)));
az=g*(nz(i)+cos(Theda(i))*sin(Gamma(i)));
csB=cos(Beta(i));
csBinv=1/csB;
ssB=sin(Beta(i));
csA=cos(Alpha(i));
ssA=sin(Alpha(i));
axv=ax/V(i);
ayv=ay/V(i);
azv=az/V(i);
Theda(i+1)=Theda(i)+dt*(((Wy_r(i)*Ery*sin(Gamma(i)))+(Wz_r(i)*Erz*cos(Gamma(i)))));
Gamma(i+1)=Gamma(i)+dt*((Wx_r(i)*Erx-(tan (Theda(i))*(Wy_r(i)*Ery*cos(Gamma(i))-Wz_r(i)*Erz*sin(Gamma(i))))));
Alpha(i+1)= Alpha(i)+ dt*( Wz_r(i)*Erz-csBinv*Erv(ssA*(axv-Wy_r(i)*Ery*ssB)+csA*(ayv+Wx_r(i)*Erx*ssB)) );
Beta(i+1)=Beta(i)+dt*( azv*csB-csA*(axv*Erv*ssB-Wy_r(i))+ssA*(ayv*ssB+Wx_r(i)*Erx) );
V(i+1)=V(i)+dt*(ax*csA*csB-ay*Erw*ssA*csB+az*ssB );
fval(1,1,:)=Theda;
fval(2,1,:)=Gamma;
fval(3,1,:)=Alpha;
fval(4,1,:)=Beta;
fval(5,1,:)=V;
end
end
The optimization file is expressed below.
-------------------------------------------------------
%Solving NLAE
clc
clear
zg=input('Enter initial guess');
format short g
%options = optimoptions('fsolve','Display','iter');
%options=optimoptions('fsolve','Algorithm','trust-region');
%options=optimoptions('fsolve','Algorithm','trust-region-dogleg');
options=optimoptions('fsolve','Algorithm','levenberg-marquardt');
%Sol=fsolve(@SimFnc,zg,options)
% @fncSi = @(t,y)myfun(t,y,Wx,Wy,Wz);
[X,fval,exitflag,output,hessian] =fsolve(@SimFnc,zg,options)

  2 Comments

Sargondjani
Sargondjani on 21 Jan 2021
It is not clear what your problem is. Also it is helpful if you provide a denser version of your question, 90% of your code just seems to define some parameters. (ie. provide a minimum working example).
Nicholas Moung
Nicholas Moung on 21 Jan 2021
You are right. I have done the integration in decrete time and I need to identify some parameters (Erx=X(1); Ery=X(2); Erz=X(3); Erv=X(4); Erw=X(5) of the system by using fsolve function. I'm looking forward to hearing your further advise. Thank you!

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Answers (2)

Sargondjani
Sargondjani on 22 Jan 2021
It is still not clear what your problem is. Do you get an error? Do you get a different solution than you expected?
Anyway fsolve will try to find the zeros of the output, but your output are large vectors, so they can not all be zero by setting 5 parameters. In that case it is probably better to use the function 'lsqnonlin'.
Other notes:
  • you should preallocate variables: Theda = NaN(1,2002+1); before the loop;
  • if you use lsqnonlin, i would recommend to use output arguments in a matrix (not 3d array): fval(1,:) = Theda;

  1 Comment

Nicholas Moung
Nicholas Moung on 1 Feb 2021 at 18:29
Hello Sir!
I did everything you suggested and I'm still getting some errors as expressed below.
Array indices must be positive integers or logical values.
Error in SimFnc5 (line 74)
Alpha(i+1)= Alpha(i)+ dt*( Wz_r(i)*Erz-csBinv*Erv(ssA*(axv-Wy_r(i)*Ery*ssB)+csA*(ayv+Wx_r(i)*Erx*ssB)) );
Error in fsolve (line 242)
fuser = feval(funfcn{3},x,varargin{:});
Error in Sol_SimFnc (line 12)
[X,fval,exitflag,output,hessian]=fsolve(@SimFnc5,zg,options)%jacobian,
Caused by:
Failure in initial objective function evaluation. FSOLVE cannot continue.
Could you please tell me what to do further? Thank you so much!

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