Exact Computation of Maximal Invariant Sets for Safe Markov Chains—Lattice Theoretic Approach - ENAC - École nationale de l'aviation civile Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2022

Exact Computation of Maximal Invariant Sets for Safe Markov Chains—Lattice Theoretic Approach

Dylan Janak
Behcet Ackmese

Résumé

Set theoretic analysis plays a crucial part in understanding safety requirements for control systems. We apply the lattice theoretic insights of fixed point theorems to construct the maximal invariant set and verify safety constraint satisfaction. We present a Kleene iteration-based algorithm with a novel initialization—based on omega-limit sets—for exactly computing the maximal invariant set under a general safety constraint, and we analyze this algorithm for the special case of Markov chains under polyhedral safety constraints. We also establish sufficient conditions for finite termination of the for a general discrete-time system, which is applicable to Markov chains. In addition to proving that the new initialization of the Kleene iteration algorithm requires no more iterations than the previously considered initialization, we present an example where our method computes the exact maximal invariant set in finitely many iterations and the previous method does not.
Fichier non déposé

Dates et versions

hal-04051117 , version 1 (29-03-2023)

Identifiants

Citer

Dylan Janak, Pierre-Loïc Garoche, Behcet Ackmese. Exact Computation of Maximal Invariant Sets for Safe Markov Chains—Lattice Theoretic Approach. IEEE Transactions on Automatic Control, 2022, 67 (12), pp.6980-6986. ⟨10.1109/TAC.2022.3211959⟩. ⟨hal-04051117⟩

Collections

ENAC ANR
11 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More