Reliable solution of special event location problems for ODEs
ACM Transactions on Mathematical Software (TOMS)
State event location in differential-algebraic models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Nonlinear Control Systems
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Verification of Polyhedral-Invariant Hybrid Automata Using Polygonal Flow Pipe Approximations
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
An Overview of Hybrid Simulation Phenomena and Their Support by Simulation Packages
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Level Set Methods for Computation in Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Modular Specification of Hybrid Systems in CHARON
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Hierarchical Hybrid Modeling of Embedded Systems
EMSOFT '01 Proceedings of the First International Workshop on Embedded Software
Visual Programming for Modeling and Simulation of Biomolecular Regulatory Networks
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
Falsification of LTL Safety Properties in Hybrid Systems
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Parameter Synthesis for Hybrid Systems with an Application to Simulink Models
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Electronic Notes in Theoretical Computer Science (ENTCS)
Object-oriented formal modeling and analysis of interacting hybrid systems in HI-maude
SEFM'11 Proceedings of the 9th international conference on Software engineering and formal methods
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Operational semantics of hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side
Journal of Computational and Applied Mathematics
A toolbox for simulation of hybrid systems in matlab/simulink: hybrid equations (HyEQ) toolbox
Proceedings of the 16th international conference on Hybrid systems: computation and control
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It has been observed that there are a variety of situations in which the most popular hybrid simulation methods can fail to properly detect the occurrence of discrete events. In this paper, we present a method for detecting discrete which, using techniques borrowed from control theory, selects integration step sizes in such a way that the simulation slows down as the state approaches a set which triggers an event (a guard set). Our method guarantees that the state will approach the boundary of this set exponentially; and in the case of linear or polynomial guard descriptions, terminating on it, without entering it. Given that any system with a nonlinear guard description can be transformed to an equivalent system with a linear guard description, this technique is applicable to a broad class of systems. Even in situations where nonlinear guards have not been transformed to the canonical form, the method is still increases the chances of detecting and event in practice. We show how to extend the method to guard sets which are constructed from many simple sets using boolean operators (e.g. polyhedral or semi-algebraic sets) . The technique is easily used in combination with existing numerical integration methods and does not adversely affect the underlying accuracy or stability of the algorithms.