Invariant Sets for Switching Affine Systems Subject to Semi-Algebraic Constraints

Athanasapoulos, Nikolaos;Jungers, Raphaël
(2016) International Federation of Automatic Control 20th IFAC Symposium on Automatic Control in Aerospace - ACA 2016 — Location: Sherbrooke, Quebec, Canada (21.August.2016)

Files

No attached file found for this publication.

Details

Authors
  • Athanasapoulos, NikolaosQueen's University Belfast
    Author
  • Jungers, RaphaëlUCLouvain
    Author
Abstract
We study the problem of computing the maximal admissible positively invariant set for discrete time switching affine systems subject to basic semi-algebraic constraints. First, we obtain inner ϵ-approximations of the minimal invariant set. Second, following recent results for switching linear systems (Athanasopoulos and Jungers, 2016), we apply an algebraic lifting on the system and obtain a polyhedral representation of the constraint set. Working on this lifted state space offers two distinct advantages, namely (i) we can verify inclusion of an e-inflation of the minimal invariant set in the constraint set and (ii) under proper assumptions, we can characterize and compute the maximal admissible invariant set, which is also a basic semi-algebraic set. Consequently, we are able to identify and recover admissible invariant sets for switching affine systems even when only non-convex invariant sets exist. The underlying algorithms involve only linear operations and convex hull computations.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Athanasapoulos, N., & Jungers, R. (2016). Invariant Sets for Switching Affine Systems Subject to Semi-Algebraic Constraints. IFAC Proceedings, 49, 158-163. https://hdl.handle.net/2078.5/52173 (Original work published 2016)