Efficient optimal prioritized infeasibility handling in model predictive control - a parametric preemptive multi-objective linear programming approach

All practical model based control (MPC) implementations should have a means to recover from infeasibility. We propose a strategy designed for liner state-space MPC with prioritized constraints. It optimally relaxes an infeasible MPC optimization problem into a feasible one by solving a single-objective linear program (LP) on-line in addition to the standard on-line MPC optimization problem at each sample. By optimal it is meant that the violation of a lower prioritized constraint cannot be made les without increasing the violation of a higher prioritized constraint. The problem of computing optimal constraint violations is naturally formulated as a parametric preemptive multi-objective LP. By extending well known results from parametric LP, the preemptive multi-objective LP is reformulated into an equivalent standard singlke-objective LP. An efficient algorithm for off-line design of this LP is given, and the algorithm is illustrated on an example.