Hi
You have created non-stationary shocks for G
log(mu_A)=LambdaA+epsA;
log(mu_G)=LambdaG+epsG;
//28. Defininition composite technology
mu_z=mu_A^(1/(1-alppha))*mu_I^(alppha/(1-alppha));
mu_G=mu_z;
This seems unconventional and I am not sure whether a balanced growth path exists given your functional forms and other non-stationary technology shocks in your model.
Usually G is given a stationary shock like the one that you have created for the labour shock.
log(G)=rhoG*log(G(-1))+epsG;
Cheers
Reuben