The Akishop PS360+ is an incredibly versatile controller, though it can be troublesome to upgrade if you're not certain of the process.
Lab Zero - developers behind fighting game Skullgirls - created a patch that allows older PS3-based joysticks to work with the console. This is built into certain games that allow for its use. Other games that do not have this patch are limited to a timeout period of eight minutes.
Anomaly Arcade Sticks helps break down the steps needed to upgrade the firmware, allowing you to control the new PS4 console. Check out the instructables article here: