Formal analysis of piecewise affine systems through formula-guided refinement

Authors:
Boyan Yordanov;Jana Tmová;Ivana Erná;Jiří Barnat;Calin Belta
Affiliations:
Department of Mechanical Engineering, Boston University, United States;Department of Mechanical Engineering, Boston University, United States;Department of Informatics, Masaryk University, Czech Republic;Department of Informatics, Masaryk University, Czech Republic;Department of Mechanical Engineering and Division of Systems Engineering, Boston University, United States
Venue:
Automatica (Journal of IFAC)
Year:
2013

Citing 8
Cited 0

Lightweight Reasoning about Program Correctness

Information Systems Frontiers
Formula-Dependent Equivalence for Compositional CTL Model Checking

Formal Methods in System Design
Model Checking Partial State Spaces with 3-Valued Temporal Logics

CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
A classification of symbolic transition systems

ACM Transactions on Computational Logic (TOCL)
Dealing with Nondeterminism in Symbolic Control

HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Comparison of four procedures for the identification of hybrid systems

HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Brief Equivalence of hybrid dynamical models

Automatica (Journal of IFAC)
Bisimilar linear systems

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.14

Visualization

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.