  The paper concerns the necessary maximum principle for robust optimal control
problems of quadratic BSDEs. The coefficient of the systems depends on the
parameter $\theta$, and the generator of BSDEs is of quadratic growth in $z$.
Since the model is uncertain, the variational inequality is proved by weak
convergence technique. In addition, due to the generator being quadratic with
respect to $z$, the forward adjoint equations are SDEs with unbounded
coefficient involving mean oscillation martingales. Using reverse H\"older
inequality and John-Nirenberg inequality, we show that its solutions are
continuous with respect to the parameter $\theta$. The necessary and sufficient
conditions for robust optimal control are proved by linearization method.
