Elimination of Redundant Polynomial Constraints and Its Use in Constrained Control

TL;DR

This paper introduces a novel Sum of Squares-based method for detecting and eliminating redundant polynomial constraints, improving computational efficiency in constrained control applications like MPC and Reference Governors.

Contribution

The paper presents a new methodology for removing redundant non-linear polynomial constraints using Sum of Squares, applicable to control problems and independent of cost functions.

Findings

Redundant polynomial constraints can be effectively eliminated.

The method reduces computational burden in MPC and Reference Governor algorithms.

Terminal constraints in MPC can be eliminated simply and independently of the cost function.

Abstract

The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect redundant non-linear constraints is an open problem. In this paper we present a novel methodology based on Sum of Squares for the elimination of redundant polynomial constraints. The paper also presents some relevant applications of the presented method to constrained control problems. In particular, we show how the proposed method can be used in the Model Predictive Control and in the Reference Governor frameworks to reduce the computational burden of the online algorithms. Furthermore, this method can also be used to eliminate the terminal constraints in MPC in a simple way that is independent from the cost function.