Katy Perry Leaving for Ariana Grande Manchester Concert Half Asleep

Katy Perry just left for Manchester ahead of her performance alongside Ariana Grande -- but she looks half asleep ... with a full bedtime getup.

Paps got Katy leaving Paris Sunday morning to board a private jet as she prepared to join Ariana, Justin Bieber and the rest of the star-studded lineup for One Love Manchester.

Unfortunately, Katy looks like she didn't get a good night's sleep. She's got PJs on ... including a pillow and a teddy bear with her too.