On the computation of lambda-contractive sets for linear constrained systems

TL;DR

This paper introduces methods to compute and approximate lambda-contractive sets for constrained linear systems, enabling better control invariant set estimation with guaranteed precision and iteration bounds.

Contribution

It provides a priori iteration bounds for approximating maximal lambda-contractive sets and a procedure to select lambda for accurate approximation of controlled invariant sets.

Findings

A method to determine the number of iterations needed for approximation.

A procedure to choose lambda ensuring approximation accuracy.

Theoretical guarantees for set approximation precision.

Abstract

We present two theoretical results on the computation of lambda-contractive sets for linear systems with state and input constraints. First, we show that it is possible to a priori compute a number of iterations that is sufficient to approximate the maximal lambda-contractive set with a given precision using 1-step sets. Second, based on the former result, we provide a procedure for choosing lambda so that the associated maximal lambda-contractive set is guaranteed to approximate the maximal controlled invariant set with a given accuracy.