irafhy
Interval arithmetic based Reachability Analysis Framework for Hybrid Automaton
under approximation backward reach-ability analysis of example 5 using interval hull

System

HYBRID_AUTOMATON
{
NAME Example Model
VARIABLES
{
x1, x2
}
LOCATIONS
{
MODEL
{
NAME controller
FLOWS
{
x1' = x2
x2' = -0.2*(x1^2-1)*x2-x1
}
INVARIANT_CONDITIONS
{
}
}
}
TRANSITIONS
{
}
}

Setting

SETTINGS
{
TIME_HORIZON := [0,2.3]
STEP := 0.01
GEOMETRY := INTERVAL_HULL
PLOT := ON
PRINT := OFF
ANALYSIS := FORWARD #invalid setting, we force backward in the Analyser
MAX_JUMP := 1
START_MODEL_ID := controller #name of the model
INITIAL_CONDITION :=
CONDITION
{
INTERVAL_HULL
{
[1.2,1.5],
[0.8,1.1]
}
}
}

Result

here are some screenshots of the results

3d
0
1
2