I doubt it, would rather they continue to focus on PS4.

People need to remember the psp was a huge seller and a very successful portable and rather a clunky design with its it's umd drive and relatively short battery life. There is no reason Sony can't compete and even outsell Nintendo in this sector.

There are lots of advantages Sony can bring to their new portable including a platform that is easy to migrate titles to, third party support, more competitive pricing, not huge licensing costs from nvidia, better controls, superior online functionality, integrating with home consoles.

It's really more about getting the product and marketing right rather than some sort of consumer resistance to Sony as a portable console brand. Sony only has to offer portable performance at Switch level which is easy to do. It doesn't have to provide a enhanced docked mode.

It will be commercially clear that if the Switch continues to sell well and there isnt a sales drop off that the hybrid format is a winner and Sony will need to at least try to stop a large migration of Sony users going to Nintendo who decide they do want both a portable and home console that runs the same software. It's not like they can ignore it they have to try to make something more appealing to end consumers to compete with Switch. It's commercial reality.

Looking at the track records, the weakest platform PlayStation ever had still beat out the Wii U and the Virtual Boy. History says yes.

A 7nm mobile device running on PS4 tech should be possible around late 2019 or 2020. 

There are very few Tablets/Hybrids running AMD right now, and no phones that I know of. AMD has not been in a great position the last few years, and only now are they starting to regain some footing. Their Ryzen based mobile CPU's, and their Navi based GPU's should both go a long ways towards bringing PS4 level power in the 10 Watt range.

I fully expect Sony to get access to 7nm chips before AMD announces their successor to Raven Ridge. Like I said, I think 2019 is very reasonable, but they it could take until 2020.

AMD and Sony are both in the best positions they have been in, in nearly a decade. Sony is on pace to be the most successful they ever have. There is a lot more money going into PlayStation R&D now than there was during the inital PS4 phase, and Sony knows they have to continue to innovate to keep the momentum going. AMD knows they have to become viable in the mobile space if they want to continue to grow as well. A lot of time is being spent increasing performance per watt, some of which we have already seen, and we will see even more with Zen+ and Navi.

Wii U, Virtual boy >>>>> PSP Go

PSPgo was a sku, not a platform.

Yes but the psp go was the biggest failure since the virtual boy

1. The biggest failed platform since VB is Wii U

2. Sales numbers for the PSPgo are lumped in with the four other versions of the device, so determining whether or not it sucked more than, say, GBA Micro is just about impossible.

1. nope

2. maybe but I daubt PSP Go sold more - "GBA Micro: 2.42 million(as of March 31, 2007)

Even if 7nm is doable, the current PS4 at 16nm runs at over 55 watts. 

Assuming a die shrink brings that down by half, you are still over 25 watts consumption, which is way too hot for a mobile device. 

Beyond that, Nintendo themselves could easily counter with a Tegra X3 chip that would allow for PS4-tier graphics PLUS Nintendo exclusives (Pokmeon, Mario, Zelda, Splatoon, Animal Crossing, Smash, Mario Kart, etc.) AND backwards compatibility with by then probably like 1000+ Switch games. 

Sony is screwed either way. They can't compete with Nintendo, especially since they will never support a portable in the main way Nintendo supports theirs. You'll only get old/spin-off crappier versions of Sony console titles whereas Nintendo puts their main teams and puts real installments of their main games on the Switch platform. 

Is Sony going to move Uncharted 5 or 6 from the main Naughty Dog team away from PS5 to put it on PSP3? Hell no.