A characterization of the groups $PS{L}_n(q)$ and $PS{U}_n(q)$ by their $2$-fusion systems, $q$ odd

Let $q$ be a nontrivial odd prime power, and let $n\ge 2$ be a natural number with $(n,q)\mathrm{\ne }(2,3)$. We characterize the groups $PS{L}_n(q)$ and $PS{U}_n(q)$ by their $2$-fusion systems. This contributes to a programme of Aschbacher aiming at a simplified proof of the classification of finite simple groups.