You can try using WMI:
$command = "notepad.exe"
$process = [WMICLASS]"\\$CompName\ROOT\CIMV2:win32_process"
$result = $process.Create($command)
If you need passing credentials:
$cred = get-credential
$process = get-wmiobject -query "SELECT * FROM Meta_Class WHERE __Class = 'Win32_Process'" -namespace "root\cimv2" -computername $CompName -credential $cred
$results = $process.Create( "notepad.exe" )