https://en.wikipedia.org/wiki/Model_predictive_control

the links above describes quite well the principle of MPC programming and the main differences with PID controlling technique.

In some way, MPC is an 'enlargement' of PID controlling technique, preferable to use when systems to be controlled are more complicated ; it can use in its turn PID parameters as part of its variables, so the work you have previously done wiith PID algos can be useful