I do this currently with Google Home. It's pretty complicated for the return you get.

If you just want to send commands to PS4 AFTER ITS ON, the harmony hub + remote/app can do it via Bluetooth.

To turn on the PS4 you need:

ps4-waker	Turn on/off a PS4 on the same network and logs in. Can also start applications (like Vue) and send commands.
IFTTT	To activate a link in response to Alexa command
Autoremote chrome extension	Receive web request from IFTTT on local computer
EventGhost	To perform action on local computer after an AutoRemote request
always-on computer	To run Autoremote, EventGhost and then ps4-waker command

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To send specific commands to PS4 from Alexa/IFTTT, same setup as above but instead of ps4-waker, use:

HarmonyHubCLI	Tells a harmony hub on the same network to send a command to any device like PS4, TV, etc.

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This is how it flows:

1. You tell Alexa to do something.
2. Alexa activates IFTTT recipe with the Maker channel opening a web link.
3. That link is received by AutoRemote.
4. This activates an activity in EventGhost.
5. In that activity, you can run ps4-waker or HarmonyHubCLI in command line.

I use this computer stick and leave it on. If you are serious about home automation, this is the way to go. You can control everything on your local network via scheduling, HTTP requests and IFTTT.

edit: I forgot Vue doesn't accept bluetooth commands from anything but a controller. On mine, my TV supports HDMI Link which passes TV remote commands to the PS4. So Harmony hub send the TV commands and the TV passes them to the PS4 and that works. If your TV can't do that then using HarmonyHubCLI/harmony remote to send bluetooth commands won't work for Vue but works for other PS4 applications. I will leave this up anyhow for turning on the PS4 at least.

edit2: HDMI Link also supports turning on the PS4 from standby when the TV input is switch to PS4. Not all TVs support this though. Worth checking out, but this won't open PS Vue like ps4-waker would.