Symmetric Linear Model Predictive Control

This paper studies symmetry in linear model predictive control (MPC). We define symmetry for model predictive control laws and for model predictive control problems. Properties of both MPC symmetries are studied by using a group theory formalism. We show how to efficiently compute MPC symmetries by transforming the search of MPC symmetry generators into a graph automorphism problem. MPC symmetries are then used to design model predictive control algorithms with reduced complexity. The effectiveness of the proposed approach is shown through a simple large-scale MPC problem whose explicit solution can only be found with the method presented in this paper.

I. Introduction

THE main idea of predictive control is to use a model of the plant to predict its future evolution. At each sampling time, starting at the current state, an open-loop optimal control problem is solved over a finite horizon. The optimal command signal is applied to the process only during the following sampling interval. At the next time step, a new optimal control problem based on new measurements of the state is solved over a shifted horizon. The resultant control algorithm is referred to as Model Predictive Control (MPC). The popularity of MPC stems from the fact that the resulting operating strategy respects all the system constraints. This is difficult to accomplish using other control techniques. One limitation of this approach is that running the optimization algorithm on-line at each time step requires substantial time and computational resources.