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Formal analysis of piecewise affine systems through formula-guided refinement |
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| Authors: | Boyan Yordanov Jana Tůmová Ivana Černá Jiří Barnat Calin Belta |
| Affiliation: | 1. Department of Mechanical Engineering, Boston University, United States;2. Department of Informatics, Masaryk University, Czech Republic;3. Department of Mechanical Engineering and Division of Systems Engineering, Boston University, United States;1. DIAM, Seconda Università degli Studi di Napoli and CREATE consortium, Italy;2. DIMET, Università degli Studi “Mediterranea” di Reggio Calabria and CREATE consortium, Italy;3. DEIS, Università degli Studi della Calabria, Italy;1. United Technologies Research Center, East Hartford, CT 06108, USA;2. Center for Control Dynamical Systems and Computation, University of California, Santa Barbara, CA 93106, USA;1. Université de Lorraine, CRAN, UMR 7039, 2 avenue de la forêt de Haye, Vand?uvre-lès-Nancy Cedex, 54516, France;2. CNRS, CRAN, UMR 7039, France;3. SATIE, ENS Cachan, CNRS, 61 av du President Wilson, F-94230 Cachan, France;4. DAS-CTC-UFSC, P.O. Box 476, 88040-900 Florianópolis, SC, Brazil |
| Abstract: | 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. |
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