Theoretical Computer Science
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Symbolic Algorithms for Infinite-State Games
CONCUR '01 Proceedings of the 12th International Conference on Concurrency Theory
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Acta Informatica - Hybrid Systems
Abstractions for hybrid systems
Formal Methods in System Design
Approximating Continuous Systems by Timed Automata
FMSB '08 Proceedings of the 1st international workshop on Formal Methods in Systems Biology
Progress on reachability analysis of hybrid systems using predicate abstraction
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Verification, performance analysis and controller synthesis for real-time systems
FSEN'09 Proceedings of the Third IPM international conference on Fundamentals of Software Engineering
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Dynamically-Driven timed automaton abstractions for proving liveness of continuous systems
FORMATS'12 Proceedings of the 10th international conference on Formal Modeling and Analysis of Timed Systems
ACM Computing Surveys (CSUR)
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This paper presents a method for abstracting continuous dynamical systems by timed automata. The abstraction is based on partitioning the state space of a dynamical system using positive invariant sets, which form cells that represent locations of a timed automaton. The abstraction is intended to enable formal verification of temporal properties of dynamical systems without simulating any system trajectory, which is currently not possible. Therefore, conditions for obtaining sound, complete, and refinable abstractions are set up.The novelty of the method is the partitioning of the state space, which is generated utilizing sub-level sets of Lyapunov functions, as they are positive invariant sets. It is shown that this partition generates sound and complete abstractions. Furthermore, the complete abstractions can be composed of multiple timed automata, allowing parallelization of the verification process. The proposed abstraction is applied to two examples, which illustrate how sound and complete abstractions are generated and the type of specification we can check. Finally, an example shows how the compositionality of the abstraction can be used to analyze a high-dimensional system.