Efficient infeasibility handling in linear MPC subject to prioritized constraints

All practical MPC implementations should have a means to recover from infeasibility. We propose an algorithm designed for linear state-space MPC which optimally relaxes an infeasible prioritized MPC optimization problem into a feasible one by solving only one LP on-line in addition to the standard MPC optimization problem. By optimal it is meant that the violation of a lower prioritized constraint cannot be made less without increasing the violation of a higher prioritized constraint. It is shown how to design the LP off-line such that the computed constraint violations are optimal.