A Polytopic Invariant Set Based Iterative Learning Model Predictive Control

Abstract

Model predictive control (MPC) is often combined with iterative learning control (ILC), which results in the so-called iterative learning model predictive control (ILMPC), to control batch processes with constraints. It is a long-standing and challenging problem that how to simultaneously guarantee system stability and constraint satisfaction in ILMPC design. Several invariant set-based methods, such as the zero-terminal state and the ellipsoidal invariant set, have been proposed to solve this problem. However, these methods are often restrictive with conservative control performance and limited applicability. In this paper, we propose a polytopic invariant set based ILMPC method to reduce conservativeness. Specifically, a polytopic invariant set is designed based on geometric computation and proved to be convex and compact. An iterative algorithm is proposed to compute the maximal one. Numerical simulations are provided to demonstrate its effectiveness.