A One-step Approach to Computing a Polytopic Robust Positively Invariant Set

TL;DR

This paper introduces a one-step linear programming method to compute the minimal robust positively invariant set for linear systems with disturbances, simplifying the process and ensuring minimality within a specified family.

Contribution

It presents a novel single LP approach for efficiently computing minimal polytopic RPI sets with theoretical guarantees.

Findings

The method computes minimal RPI sets via a single LP.

The approach guarantees minimality within a predefined family of sets.

Theoretical results support the validity of the procedure.

Abstract

A procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant (RPI) set for a linear discrete-time system subject to unknown, bounded disturbances. The procedure computes, via the solving of a single LP, a polytopic RPI set that is minimal with respect to the family of RPI sets generated from a finite number of inequalities with pre-defined normal vectors.