A Reference Governor for linear systems with polynomial constraints

TL;DR

This paper introduces a new reference governor approach for linear discrete-time systems with polynomial constraints, utilizing a nonlinear optimization and bisection algorithm to compute invariant sets, demonstrated through numerical examples.

Contribution

A novel algorithm for computing maximal output admissible invariant sets under polynomial constraints in linear systems is proposed.

Findings

Effective computation of invariant sets demonstrated

Algorithm outperforms traditional methods in examples

Applicable to systems with polynomial inequality constraints

Abstract

The paper considers the application of reference governors to linear discrete-time systems with constraints given by polynomial inequalities. We propose a novel algorithm to compute the maximal output admissible invariant set in the case of polynomial constraints. The reference governor solves a constrained nonlinear minimization problem at initialization and then uses a bisection algorithm at the subsequent time steps. The effectiveness of the method is demonstrated by two numerical examples.