Is it possible to restart server from ASP.NET application that is hosted by LocalSystem or LocalService account? This is working when I create custom administrative account
You could have your code impersonate a specific account when making that call or stand up a web service with one account. I recommend the web service, worst case is you update one app pool. You could also lock down the web service internally to only your applications.
A small C# Class for impersonating a User