Low-complexity polynomial approximation of explicit MPC via linear programming

This paper addresses the issue of the practical implementation of Model Predictive Controllers (MPC) to processes with short sampling times. Given an explicit solution to an MPC problem, the main idea is to approximate the optimal control law defined over state space regions by a single polynomial of pre-specified degree which, when applied as a state-feedback, guarantees closed-loop stability, constraint satisfaction, and a bounded performance decay. It is shown how to search for such a polynomial by solving a single linear program.