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