On Piecewise Quadratic Terminal Costs for MPC

TL;DR

This paper introduces a new method for designing terminal costs and regions in linear MPC that expand the stability region and reduce suboptimality, using configuration-constrained polytopic methods.

Contribution

It proposes a novel construction of terminal regions and costs that match the infinite-horizon LQR cost locally, improving MPC stability and performance.

Findings

Enhanced region of attraction in MPC schemes.

Reduced suboptimality compared to existing methods.

Validated through case studies and comparisons.

Abstract

This paper presents a novel approach to synthesize stabilizing termi- nal ingredients for linear model predictive control (MPC) schemes, with the aim of increasing the region of attraction while reducing suboptimal- ity with respect to the solution of the infinite-horizon optimal control problem. It is based on the construction of a novel terminal region using methods from the field of configuration-constrained polytopic computing, along with a terminal cost that is exactly equal to the infinite-horizon linear-quadratic regulator cost in a nontrivial neighborhood of the steady- state. The practical performance of the controller is illustrated through various case studies, and comparisons with state-of-the-art approaches are presented.