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Formal analysis of piecewise affine systems through formula-guided refinement

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YORDANOV Boyan TŮMOVÁ Jana ČERNÁ Ivana BARNAT Jiří BELTA Calin

Druh Článek v odborném periodiku
Časopis / Zdroj Automatica
Fakulta / Pracoviště MU

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Citace
Doi http://dx.doi.org/10.1016/j.automatica.2012.09.027
Obor Informatika
Klíčová slova Piecewise linear analysis; Temporal logic; Verification; Biotechnology
Popis We present a computational framework for identifying a set of initial states from which all trajectories of a piecewise affine (PWA) system with additive uncertainty satisfy a linear temporal logic (LTL) formula over a set of linear predicates in its state variables. Our approach is based on the construction and refinement of finite abstractions of infinite systems. We derive conditions guaranteeing the equivalence of an infinite system and its finite abstraction with respect to a specific LTL formula and propose a method for the construction of such formula-equivalent abstractions. While provably correct, the overall method is conservative and expensive. A tool for PWA systems implementing the proposed procedure using polyhedral operations and analysis of finite graphs is made available. Examples illustrating the analysis of PWA models of gene networks are included. (C) 2012 Elsevier Ltd. All rights reserved.
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