Discrete Simulation of Behavioural Hybrid Process Calculus

1. Discrete Simulation of Behavioural Hybrid Process Calculus Tomas Krilavičius Helen Shonenberg University of Twente

2. Outline • Motivation • Behavioural Hybrid Process Calculus • Discrete simulation • Future plans • Conclusions

3. Motivation • Formal languages • Hybrid systems: embedded systems, models in natural and social sciences • Main analysis technique for hybrid systems

4. Behavioural Hybrid Process Calculus Process algebraic theory concurrency, communication, discrete actions Behavioural theory continuous realm J.W.Polderman, J.C.Willems Introduction to Mathematical Systems Theory

5. Behavioural Hybrid Process Calculus Trajectories and their continuations • Trajectory-prefix • Superposition • Parallel composition • Separation of concerns • Bisimulation is congruence Choice is made when it is really time to do it Synchronisation on specified actions&signals Discrete and continuous behaviours can be separated syntactically Bisimilar processes can be substituted

6. Simulation of Hybrid Systems Main analysis technique for hybrid systems Discrete simulation First step to simulation of hybrid systems Provides interesting information

7. Discrete Simulation of BHPC Abstraction From Continuous Behaviour Trajectory-prefix Guard Superposition Parallel composition Technique Application of SOS rules Expansion law

8. Trajectory-prefix Special type of action-prefix silent action special action to denote trajectory-prefix special action name for each trajectory-prefix

9. Guard true false assign evaluation for each guard individually

10. Superposition, Parallel Composition trajectory-prefix is treated as action-prefix

11. Application of SOS

12. Expansion Law

13. Future Plans (I) Simulation of hybrid systems Simulation of continuous behaviour using ODE/DAE Solvers Resolving guard and parameterised action-prefix expressions Application of Expansion Law

14. Future Plans (II) “Sand-box” tool playground for hybrid phenomena investigation testing algorithms changes in language (BHPC) co-simulation

15. Future Plans (III): Visualisation q1 q2 q4 q1 q2 q3 □ □ □ □ □ □ v v Process1 a2 a3 a1 a3 v v Process2 Message Sequence Charts for discrete behaviour Graphs for continuous behaviour

16. Future Plans (IV) Model-based testing Theory for model-based testing of hybrid systems Integration with TorX (H. Bohnenkamp & A. Belinfante. Timed testing with TorX. 2005)

17. Conclusions Work in progress Abstractions of continuous behaviour Evaluation of Behavioural Hybrid Process Calculus