Let me first say that this is merely a template to explain my thoughts. Remember that HTTPS would be a must to do this.
Setting up HTTPS on your webserver is the thing u need to do.
On the server
You can place a php file called cmd.php.
In that file you could do something like:
<?php
if( get_the_argument_from_the_url_request ) {
if (argument == "telnet") {
// do your stuff
exec("telnet ...");
} else if( ... ) {
// do your stuff
exec("ssh ...");
} else... // and so forth
}
?>
On the phone
$.ajax({
url: "http://www.yourwebsite.com/?telnet=some_command",
success:function(data){
// success code here
}
});
If you want some sort of response form the server you can invoke a php script as a job when the server is rebooted.
You could create a database that the app itself and the server could write to, in order to create success/error messages.
There are ofc other solutions, but to put the idea on the table here it is.
I hope that i was of some sort of help. :)