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Commit2f29a4c

Browse files
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Merge pull request#739 from Mark-Yeatman/passivity-tools
Add passivity module, ispassive function, and passivity_test. Introduces optional dependency cvxopt.
2 parentsd98ed29 +c2255b0 commit2f29a4c

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7 files changed

+195
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lines changed

7 files changed

+195
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‎.github/workflows/python-package-conda.yml

Lines changed: 5 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -4,7 +4,7 @@ on: [push, pull_request]
44

55
jobs:
66
test-linux:
7-
name:Python ${{ matrix.python-version }}${{ matrix.slycot && format(' with Slycot from {0}', matrix.slycot) || ' without Slycot' }}${{ matrix.pandas && ', with pandas' || '' }}${{ matrix.array-and-matrix == 1 && ', array and matrix' || '' }}
7+
name:Python ${{ matrix.python-version }}${{ matrix.slycot && format(' with Slycot from {0}', matrix.slycot) || ' without Slycot' }}${{ matrix.pandas && ', with pandas' || '' }}${{ matrix.array-and-matrix == 1 && ', array and matrix' || '' }}${{ matrix.cvxopt && format(' with cvxopt from {0}', matrix.cvxopt) || ' without cvxopt' }}
88
runs-on:ubuntu-latest
99

1010
strategy:
@@ -13,6 +13,7 @@ jobs:
1313
python-version:[3.7, 3.9]
1414
slycot:["", "conda"]
1515
pandas:[""]
16+
cvxopt:["", "conda"]
1617
array-and-matrix:[0]
1718
include:
1819
-python-version:3.9
@@ -45,6 +46,9 @@ jobs:
4546
if [[ '${{matrix.pandas}}' == 'conda' ]]; then
4647
conda install pandas
4748
fi
49+
if [[ '${{matrix.cvxopt}}' == 'conda' ]]; then
50+
conda install -c conda-forge cvxopt
51+
fi
4852
4953
-name:Test with pytest
5054
env:

‎control/exception.py

Lines changed: 12 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -84,3 +84,15 @@ def pandas_check():
8484
except:
8585
pandas_installed=False
8686
returnpandas_installed
87+
88+
# Utility function to see if cvxopt is installed
89+
cvxopt_installed=None
90+
defcvxopt_check():
91+
globalcvxopt_installed
92+
ifcvxopt_installedisNone:
93+
try:
94+
importcvxopt
95+
cvxopt_installed=True
96+
except:
97+
cvxopt_installed=False
98+
returncvxopt_installed

‎control/lti.py

Lines changed: 13 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -13,6 +13,7 @@
1313
"""
1414

1515
importnumpyasnp
16+
1617
fromnumpyimportabsolute,real,angle,abs
1718
fromwarningsimportwarn
1819
from .importconfig
@@ -21,6 +22,7 @@
2122
__all__= ['poles','zeros','damp','evalfr','frequency_response',
2223
'freqresp','dcgain','pole','zero']
2324

25+
2426
classLTI(NamedIOSystem):
2527
"""LTI is a parent class to linear time-invariant (LTI) system objects.
2628
@@ -44,6 +46,7 @@ class LTI(NamedIOSystem):
4446
Note: dt processing has been moved to the NamedIOSystem class.
4547
4648
"""
49+
4750
def__init__(self,inputs=1,outputs=1,states=None,name=None,**kwargs):
4851
"""Assign the LTI object's numbers of inputs and ouputs."""
4952
super().__init__(
@@ -71,8 +74,7 @@ def _set_inputs(self, value):
7174

7275
#: Deprecated
7376
inputs=property(
74-
_get_inputs,_set_inputs,doc=
75-
"""
77+
_get_inputs,_set_inputs,doc="""
7678
Deprecated attribute; use :attr:`ninputs` instead.
7779
7880
The ``inputs`` attribute was used to store the number of system
@@ -94,8 +96,7 @@ def _set_outputs(self, value):
9496

9597
#: Deprecated
9698
outputs=property(
97-
_get_outputs,_set_outputs,doc=
98-
"""
99+
_get_outputs,_set_outputs,doc="""
99100
Deprecated attribute; use :attr:`noutputs` instead.
100101
101102
The ``outputs`` attribute was used to store the number of system
@@ -201,6 +202,11 @@ def _dcgain(self, warn_infinite):
201202
else:
202203
returnzeroresp
203204

205+
defispassive(self):
206+
# importing here prevents circular dependancy
207+
fromcontrol.passivityimportispassive
208+
returnispassive(self)
209+
204210
#
205211
# Deprecated functions
206212
#
@@ -321,7 +327,7 @@ def damp(sys, doprint=True):
321327
wn,damping,poles=sys.damp()
322328
ifdoprint:
323329
print('_____Eigenvalue______ Damping___ Frequency_')
324-
forp,d,winzip(poles,damping,wn):
330+
forp,d,winzip(poles,damping,wn):
325331
ifabs(p.imag)<1e-12:
326332
print("%10.4g %10.4g %10.4g"%
327333
(p.real,1.0,-p.real))
@@ -330,6 +336,7 @@ def damp(sys, doprint=True):
330336
(p.real,p.imag,d,w))
331337
returnwn,damping,poles
332338

339+
333340
defevalfr(sys,x,squeeze=None):
334341
"""Evaluate the transfer function of an LTI system for complex frequency x.
335342
@@ -388,6 +395,7 @@ def evalfr(sys, x, squeeze=None):
388395
"""
389396
returnsys.__call__(x,squeeze=squeeze)
390397

398+
391399
deffrequency_response(sys,omega,squeeze=None):
392400
"""Frequency response of an LTI system at multiple angular frequencies.
393401

‎control/passivity.py

Lines changed: 87 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,87 @@
1+
'''
2+
Author: Mark Yeatman
3+
Date: May 15, 2022
4+
'''
5+
6+
importnumpyasnp
7+
fromcontrolimportstatespasss
8+
9+
try:
10+
importcvxoptascvx
11+
exceptImportErrorase:
12+
cvx=None
13+
14+
15+
defispassive(sys):
16+
'''
17+
Indicates if a linear time invariant (LTI) system is passive
18+
19+
Constructs a linear matrix inequality and a feasibility optimization
20+
such that if a solution exists, the system is passive.
21+
22+
The source for the algorithm is:
23+
McCourt, Michael J., and Panos J. Antsaklis.
24+
"Demonstrating passivity and dissipativity using computational methods." ISIS 8 (2013).
25+
26+
Parameters
27+
----------
28+
sys: A continuous LTI system
29+
System to be checked.
30+
31+
Returns
32+
-------
33+
bool:
34+
The input system passive.
35+
'''
36+
ifcvxisNone:
37+
raiseModuleNotFoundError("cvxopt required for passivity module")
38+
39+
sys=ss._convert_to_statespace(sys)
40+
41+
A=sys.A
42+
B=sys.B
43+
C=sys.C
44+
D=sys.D
45+
46+
# account for strictly proper systems
47+
[n,m]=D.shape
48+
D=D+np.nextafter(0,1)*np.eye(n,m)
49+
50+
[n,_]=A.shape
51+
A=A-np.nextafter(0,1)*np.eye(n)
52+
53+
defmake_LMI_matrix(P):
54+
V=np.vstack((
55+
np.hstack((A.T @P+P@A,P@B)),
56+
np.hstack((B.T@P,np.zeros_like(D))))
57+
)
58+
returnV
59+
60+
matrix_list= []
61+
state_space_size=sys.nstates
62+
foriinrange(0,state_space_size):
63+
forjinrange(0,state_space_size):
64+
ifj<=i:
65+
P=np.zeros_like(A)
66+
P[i,j]=1.0
67+
P[j,i]=1.0
68+
matrix_list.append(make_LMI_matrix(P).flatten())
69+
70+
coefficents=np.vstack(matrix_list).T
71+
72+
constants=-np.vstack((
73+
np.hstack((np.zeros_like(A),-C.T)),
74+
np.hstack((-C,-D-D.T)))
75+
)
76+
77+
number_of_opt_vars=int(
78+
(state_space_size**2-state_space_size)/2+state_space_size)
79+
c=cvx.matrix(0.0, (number_of_opt_vars,1))
80+
81+
# crunch feasibility solution
82+
cvx.solvers.options['show_progress']=False
83+
sol=cvx.solvers.sdp(c,
84+
Gs=[cvx.matrix(coefficents)],
85+
hs=[cvx.matrix(constants)])
86+
87+
return (sol["x"]isnotNone)

‎control/tests/conftest.py

Lines changed: 2 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -17,6 +17,8 @@
1717
# pytest.param(marks=)
1818
slycotonly=pytest.mark.skipif(notcontrol.exception.slycot_check(),
1919
reason="slycot not installed")
20+
cvxoptonly=pytest.mark.skipif(notcontrol.exception.cvxopt_check(),
21+
reason="cvxopt not installed")
2022
matrixfilter=pytest.mark.filterwarnings("ignore:.*matrix subclass:"
2123
"PendingDeprecationWarning")
2224
matrixerrorfilter=pytest.mark.filterwarnings("error:.*matrix subclass:"

‎control/tests/passivity_test.py

Lines changed: 74 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,74 @@
1+
'''
2+
Author: Mark Yeatman
3+
Date: May 30, 2022
4+
'''
5+
importpytest
6+
importnumpy
7+
fromcontrolimportss,passivity,tf
8+
fromcontrol.tests.conftestimportcvxoptonly
9+
10+
11+
pytestmark=cvxoptonly
12+
13+
14+
deftest_ispassive():
15+
A=numpy.array([[0,1], [-2,-2]])
16+
B=numpy.array([[0], [1]])
17+
C=numpy.array([[-1,2]])
18+
D=numpy.array([[1.5]])
19+
sys=ss(A,B,C,D)
20+
21+
# happy path is passive
22+
assert(passivity.ispassive(sys))
23+
24+
# happy path not passive
25+
D=-D
26+
sys=ss(A,B,C,D)
27+
28+
assert(notpassivity.ispassive(sys))
29+
30+
31+
A_d=numpy.array([[-2,0], [0,0]])
32+
A=numpy.array([[-3,0], [0,-2]])
33+
B=numpy.array([[0], [1]])
34+
C=numpy.array([[-1,2]])
35+
D=numpy.array([[1.5]])
36+
37+
38+
@pytest.mark.parametrize(
39+
"test_input,expected",
40+
[((A,B,C,D*0.0),True),
41+
((A_d,B,C,D),True),
42+
((A*1e12,B,C,D*0),True),
43+
((A,B*0,C*0,D),True),
44+
((A*0,B,C,D),True),
45+
((A*0,B*0,C*0,D*0),True)])
46+
deftest_ispassive_edge_cases(test_input,expected):
47+
48+
# strictly proper
49+
A=test_input[0]
50+
B=test_input[1]
51+
C=test_input[2]
52+
D=test_input[3]
53+
sys=ss(A,B,C,D)
54+
assert(passivity.ispassive(sys)==expected)
55+
56+
57+
deftest_transfer_function():
58+
sys=tf([1], [1,2])
59+
assert(passivity.ispassive(sys))
60+
61+
sys=tf([1], [1,-2])
62+
assert(notpassivity.ispassive(sys))
63+
64+
65+
deftest_oo_style():
66+
A=numpy.array([[0,1], [-2,-2]])
67+
B=numpy.array([[0], [1]])
68+
C=numpy.array([[-1,2]])
69+
D=numpy.array([[1.5]])
70+
sys=ss(A,B,C,D)
71+
assert(sys.ispassive())
72+
73+
sys=tf([1], [1,2])
74+
assert(sys.ispassive())

‎setup.py

Lines changed: 2 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -46,6 +46,7 @@
4646
'matplotlib'],
4747
extras_require={
4848
'test': ['pytest','pytest-timeout'],
49-
'slycot': ['slycot>=0.4.0' ]
49+
'slycot': ['slycot>=0.4.0' ],
50+
'cvxopt': ['cvxopt>=1.2.0' ]
5051
}
5152
)

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