Optimal control of Euler equations of gas dynamics in Matlab - matlab

Question

I am trying to solve the optimal control for the Euler equations of gas dynamics with the cost functional of the tracking type function. The idea is optimal solutions must match the target solutions at a final time by updating the control function using the steepest descent method. I have done the program using Matlab, but the result doesn't achieve the goal; I have attached the part of the code where the issue is. The problem is mainly with the optimization loop. Any help or advice will be appreciated.
alphaAD0 = 2.9*[1,1,1]; % optim step for adjoint
ObjwAD = costfunction(rho,m,E,rhod,md,Ed,par);
for iter = 2:maxIter
alphaAD = alphaAD0;
rhoinv = rhoT(end:-1:1,:);
minv = mT(end:-1:1,:);
Einv = ET(end:-1:1,:);
[p,q] = initbackward(rho,m,E,rhod,md,Ed,par);
[pp,qq] = backwardsolve(p,q,rhoinv,minv,Einv,par);
[ADgradJrho0,ADgradJm0,ADgradJE0] = qradcost(pp,qq,rho0,m0,E0,par);
% Update data
rho00 = rho0 - alphaAD(1)*ADgradJrho0;
m00 = m0 - alphaAD(2)*ADgradJm0;
E00 = E0 - alphaAD(3)*ADgradJE0;
[rhoT,mT,ET] = forwardsolve(rho00,m00,E00,par);
rho = rhoT(end,:);
m = mT(end,:);
E = ET(end,:);
u = m./rho;
p = (par.G - 1)*(E - 0.5*rho.*u.^2);
Objfunc_1 = ObjwAD(iter-1);
Objfunc = costfunction(rho,m,E,rhod,md,Ed,par);
while Objfunc>Objfunc_1 || isnan(Objfunc)
alphaAD = alphaAD/2;
rho00 = rho0 - alphaAD(1)*ADgradJrho0;
m00 = m0 - alphaAD(2)*ADgradJm0;
E00 = E0 - alphaAD(3)*ADgradJE0;
[rhoT,mT,ET] = forwardsolve(rho00,m00,E00,par);
rho = rhoT(end,:);
m = mT(end,:);
E = ET(end,:);
u = m./rho;
p = (par.G - 1)*(E - 0.5*rho.*u.^2);
Objfunc = costfunction(rho,m,E,rhod,md,Ed,par);
end
rho0 = rho00; m0 = m00; E0 = E00;