Sony is aware of the current connection issues it is having on PSN.
They have acknowledged it on their twitter account, which we assume you can keep an eye on for updates.
We’re aware that some PSN users are experiencing connectivity issues. Thank you for your patience as we investigate.
— Ask PlayStation (@AskPlayStation) February 1, 2016
Despite this, as of this post, the official PSN service status page indicates that all services are currently up and running. This down time coming right after Ubisoft extended its closed beta for The Devision through February 2. Many people are kind of frustrated with PSN at the moment.
Lets hope they resolve this quickly. Be sure to check back for updates on this issue.