Generating invariants for non-linear hybrid systems by linear algebraic methods

Authors:
Nadir Matringe;Arnaldo Vieira Moura;Rachid Rebiha
Affiliations:
Institue de Mathematiques de Jussieu Université Paris 7, Denis Diderot, France;Institute of Computing, University of Campinas, SP, Brasil;Faculty of Informatics, University of Lugano, Switzerland and Institute of Computing, University of Campinas, SP, Brasil
Venue:
SAS'10 Proceedings of the 17th international conference on Static analysis
Year:
2010

Citing 14
Cited 1

Abstract interpretation and application to logic programs

Journal of Logic Programming
Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints

POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Introduction to Mathematical Theory of Computation

Introduction to Mathematical Theory of Computation
The theory of hybrid automata

LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Reachability of Uncertain Nonlinear Systems Using a Nonlinear Hybridization

HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Generating Box Invariants

HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Computing Differential Invariants of Hybrid Systems as Fixedpoints

CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Constraint-Based Approach for Analysis of Hybrid Systems

CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Endomorphisms for Non-trivial Non-linear Loop Invariant Generation

Proceedings of the 5th international colloquium on Theoretical Aspects of Computing
Morphisms for Non-trivial Non-linear Invariant Generation for Algebraic Hybrid Systems

HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Automatic invariant generation for hybrid systems using ideal fixed points

Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Symbolic model checking of hybrid systems using template polyhedra

TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Algorithmic algebraic model checking i: challenges from systems biology

CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Generating polynomial invariants for hybrid systems

HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control

Transcendental inductive invariants generation for non-linear differential and hybrid systems

Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control

Quantified Score

Hi-index	0.00

Visualization

Abstract

We describe powerful computational methods, relying on linear algebraic methods, for generating ideals for non-linear invariants of algebraic hybrid systems. We show that the preconditions for discrete transitions and the Lie-derivatives for continuous evolution can be viewed as morphisms and so can be suitably represented by matrices. We reduce the non-trivial invariant generation problem to the computation of the associated eigenspaces by encoding the new consecution requirements as specific morphisms represented by matrices. More specifically, we establish very general sufficient conditions that show the existence and allow the computation of invariant ideals. Our methods also embody a strategy to estimate degree bounds, leading to the discovery of rich classes of inductive, i.e. provable, invariants. Our approach avoids first-order quantifier elimination, Grobner basis computation or direct system resolution, thereby circumventing difficulties met by other recent techniques.