Computing Robust Controlled Invariant Sets of Linear Systems

TL;DR

This paper introduces two methods for computing robust controlled invariant sets in linear systems with bounded disturbances, offering precise outer and inner approximations under certain conditions.

Contribution

It presents novel algorithms for outer and inner approximations of invariant sets, including a $ extdelta$-complete outer approximation method for systems with polytope constraints.

Findings

Outer approximation can be made arbitrarily precise

Inner approximation provides guaranteed safe sets

Outer approximation is $ extdelta$-complete for polytope constraints

Abstract

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation. The outer approximation scheme is $\delta$-complete, given that the constraint sets are formulated as finite unions of polytopes.