Within _The Last Jedi_, this power is depicted as an expanded version of what Rey and Kylo had been doing throughout the film. When they're communicating through the Force, they're visible to onlookers, such as Luke:

[![Screenshot of The Last Jedi showing Luke between Rey and Kylo in a hut on Ahch-To][1]][1]

This type of communication, in turn, seems to be an expanded version of the Force communication that Luke and Leia (and Luke and Vader) are able to establish in _The Empire Strikes Back_. While this hasn't been confirmed to be the same "power", it does seem to be a difference of degree more than kind.

As for whether this exact power (projecting an "objective" image of oneself) has appeared in earlier works, TLJ director Rian Johnson mentions in _Balance of the Force_, a special feature on the Last Jedi Blu-ray, that he'd heard of a similar power from earlier Star Wars works:

> I've heard something like this described as a Force power, like actually projecting a vision of yourself elsewhere. But we've actually never seen it in the movies. It's something a little different. This could be a way that he could win this sequence.

In Legends continuity, this was known as ["Dopplegänger" (sic) or "Similfuturus"][2], and was first used (in real-world publication order) by a dark-sided Luke in 1992's _Dark Empire_ to trick Han and Leia into thinking they've rescued him:

[![Panels from Dark Empire showing Luke revealing that he's a projected image][3]][3]

Its description from the _Dark Empire_ RPG sourcebook is basically the same as what we see in _The Last Jedi_, with the caveat that it doesn't take a lethal amount of exertion to use:

> The doppleganger is an illusion, but to those who interact with it, it will seem real.  The user can sense all normal senses through the doppleganger, and the duplicate seems to have form and substance:  the doppleganger registers as normal on all droid audio and video sensors.  Those who are with the doppleganger believe it to be a real person.  The doppleganger acts with half the skill dice of the person using the power...if the Jedi stops using the power or the doppleganger is fatally injured, it simply fades away.
>
> (_The Dark Empire Sourcebook_, page 70, [source][4]) 


  [1]: https://i.sstatic.net/tigTr.jpg
  [2]: https://starwars.fandom.com/wiki/Doppleg%C3%A4nger
  [3]: https://i.sstatic.net/XsxOK.jpg
  [4]: https://web.archive.org/web/20190812065735/http://www.myuselessknowledge.com/swfa/Ret-Con.html