Completeness of Lyapunov Abstraction

@inproceedings{Wisniewski2013CompletenessOL,
  title={Completeness of Lyapunov Abstraction},
  author={Rafael Wisniewski and Christoffer Sloth},
  booktitle={HAS},
  year={2013}
}
In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines cells, which are regarded as discrete objects. The union of cells makes up the state space of the dynamical systems. Our construction gives rise to a combinatorial object - a timed automaton. We examine sound and complete abstractions. An abstraction is said… 
1 Citations

Figures from this paper

Timed Symbolic Dynamics

A theory of timed symbolic dynamics unifying results from timed automata theory and symbolic dynamics is introduced and a new measure for timed languages is provided by characterising the Gromov-Lindenstrauss-Weiss metric mean dimension for timed shift spaces.

References

SHOWING 1-10 OF 12 REFERENCES

Complete Abstractions of Dynamical Systems by Timed Automata

Abstractions for Mechanical Systems

This paper proposes a method for discretizing the state space of mechanical systems using a combination of transversal and tangential manifolds for the conservative mechanical system, to show that well-known reduction methods can be used to generate abstract models, which can beused for formal verification.

Abstractions for hybrid systems

  • A. Tiwari
  • Computer Science, Mathematics
    Formal Methods Syst. Des.
  • 2008
It is shown that the constructed abstractions are always sound, but are relatively complete only under certain assumptions, and characterize the sets of predicates that can be used to create high quality abstractions.

Geometric analysis of nondeterminacy in dynamical systems

It is shown that it is enough to consider flow lines of a single vector field in order to capture the behavior of all flow lines in the section cone up to homotopy (corresponding to equivalence of executions).

A geometric approach to bisimulation and verification of hybrid systems

  • M. Broucke
  • Computer Science
    Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)
  • 1998
The paper opens up avenues for applying model checking algorithms to the verification of safety problems for hybrid systems consisting of coordinating autonomous agents, and especially hybrid systems

A Theory of Timed Automata

SpaceEx: Scalable Verification of Hybrid Systems

We present a scalable reachability algorithm for hybrid systems with piecewise affine, non-deterministic dynamics. It combines polyhedra and support function representations of continuous sets to

Box invariance for biologically-inspired dynamical systems

An introduction to manifolds

The theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics, and one of the most basic topological invariants of a manifold, its de Rham cohomology is computed.