Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
Hybridization methods for the analysis of nonlinear systems
Acta Informatica - Hybrid Systems
Abstractions for hybrid systems
Formal Methods in System Design
Constructing invariants for hybrid systems
Formal Methods in System Design
Differential Dynamical Systems (Monographs on Mathematical Modeling and Computation)
Differential Dynamical Systems (Monographs on Mathematical Modeling and Computation)
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
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
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Computing differential invariants of hybrid systems as fixedpoints
Formal Methods in System Design
Accurate hybridization of nonlinear systems
Proceedings of the 13th ACM 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
Counter-example guided predicate abstraction of hybrid systems
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
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
Fixed point iteration for computing the time elapse operator
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
PHAVer: algorithmic verification of hybrid systems past hytech
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Safety verification of hybrid systems by constraint propagation based abstraction refinement
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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
Reachability analysis of nonlinear systems using conservative polynomialization and non-convex sets
Proceedings of the 16th international conference on Hybrid systems: computation and control
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We present abstraction techniques that transform a given non-linear dynamical system into a linear system, such that, invariant properties of the resulting linear abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change of bases transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, we present a technique to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding a linear system abstraction exists. If so, our technique yields the resulting abstract linear system, as well. This approach is further extended to search for a change of bases transformation that abstracts a given non-linear system into a system of linear differential inclusions. Our techniques enable the use of analysis techniques for linear systems to infer invariants for non-linear systems. We preesent preliminary evidence of the practical feasibility of our ideas using a prototype implementation.