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Discrete Simulation of Behavioural Hybrid Process Calculus
Tomas Krilavičius
Helen ShonenbergUniversity of Twente
2Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Outline
Motivation
Behavioural Hybrid Process Calculus
Discrete simulation
Future plans
Conclusions
Motivation
Behavioural Hybrid Process Calculus
Discrete simulation
Future plans
Conclusions
3Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Motivation
Formal languages
Hybrid systems: embedded systems,
models in natural and social sciences
Main analysis technique for hybrid
systems
Formal languages
Hybrid systems: embedded systems,
models in natural and social sciences
Main analysis technique for hybrid
systems
4Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Behavioural Hybrid Process Calculus
Process algebraic theoryconcurrency, communication,
discrete actions
Process algebraic theoryconcurrency, communication,
discrete actions
Behavioural theorycontinuous realm
J.W.Polderman, J.C.Willems Introduction to Mathematical Systems Theory
Behavioural theorycontinuous realm
J.W.Polderman, J.C.Willems Introduction to Mathematical Systems Theory
5Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Behavioural Hybrid Process Calculus
Trajectory-prefix
Superposition
Parallel composition
Separation of concerns
Bisimulation is congruence
Trajectory-prefix
Superposition
Parallel composition
Separation of concerns
Bisimulation is congruence
Trajectories and their continuations
Trajectories and their continuations
Choice is made when it is really time to do it
Choice is made when it is really time to do it
Synchronisation on specified
actions&signals
Synchronisation on specified
actions&signals
Discrete and continuous behaviours can be separated
syntactically
Discrete and continuous behaviours can be separated
syntactically
Bisimilar processes can be substituted
Bisimilar processes can be substituted
6Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Simulation of Hybrid Systems
Main analysis technique for hybrid systemsMain analysis technique for hybrid systems
Discrete simulation Discrete simulation
Provides
interesting
information
First step to
simulation of
hybrid systems
7Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Discrete Simulation of BHPC
Technique
Application of SOS rules
Expansion law
Technique
Application of SOS rules
Expansion law
Abstraction From Continuous Behaviour
Trajectory-prefix
Guard
Superposition
Parallel composition
Abstraction From Continuous Behaviour
Trajectory-prefix
Guard
Superposition
Parallel composition
8Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Trajectory-prefix
Special type of action-prefix
silent action
special action to denote trajectory-prefix
special action name for each trajectory-prefix
Special type of action-prefix
silent action
special action to denote trajectory-prefix
special action name for each trajectory-prefix
9Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Guard
falsefalsetruetrue
assign evaluation for each
guard individually
assign evaluation for each
guard individually
10Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Superposition, Parallel Composition
trajectory-prefix
is treated as
action-prefix
trajectory-prefix
is treated as
action-prefix
11Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Application of SOS
BBC
BCBBB
a
a
a
BBC
BCBBB
a
a
a
stopbroken
on
.
)On(Thermostat.
temp
stopbroken
on
.
)On(Thermostat.
temp
stopbroken
on
.
)On(Thermostat. temp
stopbroken
on
.
)On(Thermostat. temp
12Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Expansion Law
13Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
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
Simulation of hybrid systems
Simulation of continuous behaviour using
ODE/DAE Solvers
Resolving guard and parameterised action-
prefix expressions
Application of Expansion Law
14Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Future Plans (II)
“Sand-box” tool
playground for
hybrid phenomena investigation
testing algorithms
changes in language (BHPC)
co-simulation
“Sand-box” tool
playground for
hybrid phenomena investigation
testing algorithms
changes in language (BHPC)
co-simulation
15Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Future Plans (III): Visualisation
Process1
Process2
q1
q2
q3
□□□
v
v
q1
q2
q4
□□□v
v
a1 a2 a3 a3
Message Sequence Charts for discrete behaviour
Message Sequence Charts for discrete behaviour
Graphs for continuous behaviour
Graphs for continuous behaviour
16Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
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)
Model-based testing
Theory for model-based testing of hybrid systems
Integration with TorX
(H. Bohnenkamp & A. Belinfante. Timed testing with TorX. 2005)
17Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC
Conclusions
Work in progress
Abstractions of continuous behaviour
Evaluation of Behavioural Hybrid
Process Calculus
Work in progress
Abstractions of continuous behaviour
Evaluation of Behavioural Hybrid
Process Calculus
