I don't know the RoboRIO ecosystem, but I do know Linux and Java.
Code:
ssh user:password@rpihost 'sudo shutdown -h now'
You're possibly better off putting the shutdown command into a shell script so you can attempt to kill the processes 'nicely' first, then issue the shutdown - all within the script. The script would live on the raspberry pi, so your RoboRIO code doesn't have to care how the R-PI stuff shuts down, ever.
Add this when you detect end of match presuming you go the script route:
Code:
java.lang.ProcessBuilder processBuilder = new java.lang.ProcessBuilder("ssh", "user:password@rpihost","/path/to/script.bash");
java.lang.Process p = pb.start();
p.waitFor(); // WARNING - will block this thread. Also, will only block this thread.
System.out.println("R-PI shutdown executed");