This is a dicey one! As an app, you cant do much, but there is one way you can try this. Get a phone which is rooted and grants your application SuperUser permissions. Then you could try to run this piece of code from your APK.
Process mProcess = null;
DataOutputStream osStream;
try {
mProcess = Runtime.getRuntime().exec("su");
} catch (IOException e) {
Log.e("Error","Unable to get SU permissions, quitting");
}
osStream = new DataOutputStream(mProcess.getOutputStream());
try {
osStream.writeBytes("reboot");
Thread.sleep(1000);
} catch (IOException e) {
e.printStackTrace();
} catch (InterruptedException e) {
e.printStackTrace();
}
Not a tested piece of code, but hopefully should give you some idea!