Temporal Logics for Analyzing Hybrid Systems Simulation Traces

GM-CMU Collaborative Research Laboratory

Temporal Logics for Analyzing Temporal Logics for Analyzing Hybrid Systems Simulation TracesHybrid Systems Simulation Traces

GM-CMU Collaborative Research Laboratory

Sources of Simulation TracesSources of Simulation Traces• VehicleSim : A software simulator

for vehicle dynamics• Simulation Traces from MATLAB /

Simulink• Physical testing of vehicles on

roads• Hybrid Systems Visual Tools:

Ptolemy (Berkeley), CHARON (UPenn)

VehicleSim Simulator

MATLAB Simulink

PhysicalSimulation

Visual ToolsPTOLEMYCHARON

GM-CMU Collaborative Research Laboratory

Temporal LogicTemporal Logic• We can define “interesting” events and

sequence of events.– Event a does not ever happen before event b– Event a is eventually followed by event b– Event a is always accompanied by event b– Event a follows event b within two time steps.

• Forces definition of formal correctness properties– Easier-to-use sugar-coated versions like Intel’s

FORSPEC

GM-CMU Collaborative Research Laboratory

Overall System DesignOverall System DesignVehicleSim Simulator

MATLAB Simulink

PhysicalSimulation

Visual ToolsPTOLEMYCHARON

Simulation Trace

TemporalProperty

Automated Trace

Analyzer

Report

GM-CMU Collaborative Research Laboratory

ExampleExample

• Always (a <= b)

• The value of a never exceeds the value of b.

a <= b

a > b

ERROR

GM-CMU Collaborative Research Laboratory

ExampleExample

• Always (a=b X (c=100) )

• If the value of a equals the value of b, then c must take the value 100 in 1 time step.

True

a = b

c!=100c=100

Trace:

a b c

0 0 0

1 2 100

ERROR

GM-CMU Collaborative Research Laboratory

ExampleExample

• Always (a=b X (c=100) )

• If the value of a equals the value of b, then c must take the value 100 in 1 time step.

True

a = b

c!=100c=100

Trace:

a b c

0 0 0

1 2 100

ERROR

GM-CMU Collaborative Research Laboratory

ExampleExample

• Always (a=b X (c=100) )

• If the value of a equals the value of b, then c must take the value 100 in 1 time step.

True

a = b

c!=100c=100

Trace:

a b c

0 0 0

1 2 100

ERROR

GM-CMU Collaborative Research Laboratory

ExampleExample

• Always (a=b X (c=100) )

• If the value of a equals the value of b, then c must take the value 100 in 1 time step.

True

a = b

c!=100c=100

Trace:

a b c

0 0 0

1 2 99

ERROR

GM-CMU Collaborative Research Laboratory

ExampleExample

• Always (a=b X (c=100) )

• If the value of a equals the value of b, then c must take the value 100 in 1 time step.

True

a = b

c!=100c=100

Trace:

a b c

0 0 0

1 2 99

ERROR

GM-CMU Collaborative Research Laboratory

ExampleExample

• Always (a=b X (c=100) )

• If the value of a equals the value of b, then c must take the value 100 in 1 time step.

True

a = b

c!=100c=100

Trace:

a b c

0 0 0

1 2 99

ERROR

GM-CMU Collaborative Research Laboratory

Research QuestionsResearch Questions

• How to capture the continuity of trace data ?• How to capture the notion of continuous time?– Do we need a richer yet understandable logic in

line with FORSPEC for Hybrid Systems?• Online vs. Offline monitoring– If monitoring is offline, can we write efficient

algorithms that can “look into the future”

GM-CMU Collaborative Research Laboratory

Overall System DesignOverall System DesignVehicleSim Simulator

MATLAB Simulink

PhysicalSimulation

Visual ToolsPTOLEMYCHARON

Simulation Trace

TemporalProperty

Automated Trace

Analyzer

ReportYour inputs?

GM-CMU Collaborative Research Laboratory

GM-CMU Collaborative Research Laboratory

Robustness of Hybrid Systems Robustness of Hybrid Systems and Simulation Tracesand Simulation Traces

•If two traces have a prefix equivalent under a “robustness” assumption, we can combine them into an execution tree.