Efficient Off-line Solutions to Robust Model Predictive Control Using Orthogonal Partitioning

Authors:	Cychowski Marcin, Cork Institute of Technology, Ireland O'Mahony Thomas, Cork Institute of Technology, Ireland
Topic:	2.4 Optimal Control
Session:	Predictive Control
Keywords:	Model predictive control, Robust stability, Binary search trees, Linear matrix inequalities

Abstract

The main limitation of many robust model predictive control (MPC) schemes is the formidable real-time computational complexity. In this paper, a new algorithm for computing efficient approximate solutions to the min-max MPC problem for discrete-time polytopic systems is proposed. It is shown that the resulting control profile is, in fact, piecewise affine (PWA) defined on an orthogonal partition of the state space. This explicit structure is exploited for efficient real-time implementation via binary search trees. Conditions for robust exponential stability of the closed-loop system can be derived in terms of linear matrix inequality (LMI) constraints.