Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximatio
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)(πttV∆+)(πtV)(πttV
∆+
)(πtV
H10.20.22,[]m∈∧
H20.280.3,[]m∈∧
T373K=
TTalarm≥
H2H2min≤
H1H1min≤
heating
cooling/
drain T2
cooling/
drain T1
success
failure
u
1
x˙fu1x()=
xH1H2TT=
u5x˙0=u3x˙fu3x()=u
4
x˙0=
TTalarm≥
H2H2min≤
H1H1min≤
H1H1min≤
TTcrys≤∨
H1H1max≥∨
H2H2max≥
TTcrys≤∨
H1H1max≥∨
H2H2max≥
TTcrys≤∨
H1H1max≥∨
H2H2max≥
u
2
x˙fu2x()=
0
0.1
0.2
0.3
0.4
0.5
0
0.05
0.1
0.15
0.2
0.25
330
340
350
360
370
380
390
400
H1
Partition 3: Patch 2
H2
T
00.10.20.30.433034035036037038039040011H1 = 0.4H2T00.10.20.30.4
330
340
350
360
370
380
390
400
H1 = 0.04
H2
10
T
00.10.20.30.4330340350360370380390400H2 = 0.4H112T00.10.20.30.4
330
340
350
360
370
380
390
400
234H2 = 0.04H156789
T
00.10.20.30.400.050.10.150.20.250.30.350.4H1H2T = 395141316171819152000.10.20.30.4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
21
1
H1
H
2
T = 338
00.10.20.30.433034035036037038039040022H1 = 0.4H2T00.10.20.30.4
330
340
350
360
370
380
390
400
H1 = 0.04
H2
21
T
00.10.20.30.4330340350360370380390400H2 = 0.4H123T00.10.20.30.4
330
340
350
360
370
380
390
400
23
7654H2 = 0.04H11098141312111615181720
19
T
00.10.20.30.400.050.10.150.20.250.30.350.4H1H2T = 3952829243325342635273632373138303900.10.20.30.4
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
40
1
H1
H
2
T = 338