Restart-Computer remotely with Local Admin

Question

Hello;
I manage my company's server and AD infrastructure, containing hundreds of Windows 2012 R2 servers.  I also patch all of my servers monthly.  The biggest challenge in patching servers, is the fact that they need to be restarted every month, in
order for the patches to finish installing.
We have a certain group of servers, that need to have their restarts specifically scheduled.  The services offered by these servers are managed by a specific group of IT Pros.  However, this group of IT Pros do not have Local Administrative permissions
on these servers (nor do they need it to do there jobs).
I would like to enable this group to remotely restart these servers every month using the 'Restart-Computer' powershell command, without granting them Local Admin (that way, I won't need to get up at 3am every month to do this myself).  I've tried adding
them to the following "User Rights Assignment": "Force shutdown from a remote system" and "Shut down the system".
But, they still get an "Access Denied" error message.  What am I missing?  Is this even possible?  I've searched for hours now, but with no luck.

Answer 1

Thank you for the reply, but I had already tried those suggestions.  Here's what I've tried so far:
First, as I mentioned before, I've added the admins to the following "User Rights Assignment": "Force shutdown from a remote system" and "Shut down the system".  Then I temporarily added the admins to the "Allow log
on locally" user rights assignment so that I may log on to the server as the admins and prove that the admins can indeed restart the local server.  From the server console, the admin was able to launch a powershell session and run the "Restart-Computer"
command, and the server restarted perfectly. 
So that part worked just fine.  But I would like to get the admins to remotely restart the servers, without granting them the "Allow log on locally".  Another thing I tried, was to create a new remote PSSession, and then run the Restart-Computer
command from there.  At first, the New-PSSession gave me an access denied error message.  That's when I ran the Get-PSSessionConfiguration command, and I noticed that the "Builtin\Remote Management Users" group was allowed access. 
So I added the Admins to that group on one of the servers.  Now the New-PSSession command worked.  But the Restart-Computer still gives me an Access Denied error message.
Here are the commands that I am using.
First, running the Restart-Computer from the admin's workstation:
Restart-Computer -ComputerName SERVER01
Second, running the Restart-Computer command from with a remote PSSession.
New-PSSession -ComputerName SERVER01
Enter-PSSession 2
Restart-Computer
Either way, I get an access denied message.