Invariant Sets for Switching Affine Systems Subject to Semi-Algebraic Constraints
(2016) IFAC-PapersOnLine — Vol. 49, p. 158-163 (2016)
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- 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.
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Athanasopoulos, N., & Jungers, R. (2016). Invariant Sets for Switching Affine Systems Subject to Semi-Algebraic Constraints. IFAC-PapersOnLine, 49, 158-163. https://doi.org/10.1016/j.ifacol.2016.10.156 (Original work published 2016)