If it's a process that it's monitoring, you'd have to write a batch file that SolarWinds could then use via powershell to start the process. However, oftentimes, the process will stop after the remote connection is released by SolarWinds. What I've had to find, as we have a similar issue, is if there is a way to silently start the specific process by calling the exe itself. Currently I haven't had success with it for the program I'm working with, but if there is a way to do a silent start, then you could use powershell to run the batch file.
This can be done, but it is kind of messy. (Assuming you are on Windows nodes)
How we do it is we have SAM run a VBScript component monitor which checks WMI for the service status and if it is not running it will use the VBScript Wbem service (on the Win32_ScheduledJob service) Object to create a Scheduled Task job on the node (runs only once) which runs a local script (which you have to create and house locally on the node) to restart the services. My VBScript is robust enough to check and see if the local script is already running so it does not try to start unless it is not already running.
If you want to see my VBScript let me know and I can post it if you desire.