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Improved speed of ctrb and obsv functions #941

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Merged
merged 8 commits into from
Dec 1, 2023
Merged

Improved speed of ctrb and obsv functions #941

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5692317
improved speed to construct observability matrix by reducing matrix e…
Jpickard1 Nov 25, 2023
95ab229
improved time to create controllability matrix, fix to obsv function …
Jpickard1 Nov 25, 2023
7feeb2c
fixed differentce between ctrb and obsv
Jpickard1 Nov 25, 2023
bfc7e6b
Update control/statefbk.py
Jpickard1 Nov 27, 2023
44d57ac
Update control/statefbk.py
Jpickard1 Nov 27, 2023
cb4f7d9
changed doc string
Jpickard1 Nov 27, 2023
49779aa
Merge branch 'main' of https://github.com/Jpickard1/python-control
Jpickard1 Nov 27, 2023
f8ba0d9
test cases added for t < A.shape[0]
Jpickard1 Nov 27, 2023
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34 changes: 26 additions & 8 deletions control/statefbk.py
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Original file line number Diff line number Diff line change
Expand Up @@ -990,13 +990,15 @@ def _control_output(t, states, inputs, params):
return ctrl, closed


def ctrb(A, B):
def ctrb(A, B, t=None):
"""Controllabilty matrix.

Parameters
----------
A, B : array_like or string
Dynamics and input matrix of the system
t : None or integer
maximum time horizon of the controllability matrix, max = A.shape[0]

Returns
-------
Expand All @@ -1016,22 +1018,30 @@ def ctrb(A, B):
amat = _ssmatrix(A)
bmat = _ssmatrix(B)
n = np.shape(amat)[0]
m = np.shape(bmat)[1]

if t is None or t > n:
t = n

# Construct the controllability matrix
ctrb = np.hstack(
[bmat] + [np.linalg.matrix_power(amat, i) @ bmat
for i in range(1, n)])
ctrb = np.zeros((n, t * m))
ctrb[:, :m] = bmat
for k in range(1, t):
ctrb[:, k * m:(k + 1) * m] = np.dot(amat, ctrb[:, (k - 1) * m:k * m])

return _ssmatrix(ctrb)


def obsv(A, C):
def obsv(A, C, t=None):
"""Observability matrix.

Parameters
----------
A, C : array_like or string
Dynamics and output matrix of the system

t : None or integer
maximum time horizon of the controllability matrix, max = A.shape[0]

Returns
-------
O : 2D array (or matrix)
Expand All @@ -1050,10 +1060,18 @@ def obsv(A, C):
amat = _ssmatrix(A)
cmat = _ssmatrix(C)
n = np.shape(amat)[0]
p = np.shape(cmat)[0]

if t is None or t > n:
t = n

# Construct the observability matrix
obsv = np.vstack([cmat] + [cmat @ np.linalg.matrix_power(amat, i)
for i in range(1, n)])
obsv = np.zeros((t * p, n))
obsv[:p, :] = cmat

for k in range(1, t):
obsv[k * p:(k + 1) * p, :] = np.dot(obsv[(k - 1) * p:k * p, :], amat)

return _ssmatrix(obsv)


Expand Down
16 changes: 16 additions & 0 deletions control/tests/statefbk_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -49,6 +49,14 @@ def testCtrbMIMO(self):
Wc = ctrb(A, B)
np.testing.assert_array_almost_equal(Wc, Wctrue)

def testCtrbT(self):
A = np.array([[1., 2.], [3., 4.]])
B = np.array([[5., 6.], [7., 8.]])
t = 1
Wctrue = np.array([[5., 6.], [7., 8.]])
Wc = ctrb(A, B, t=t)
np.testing.assert_array_almost_equal(Wc, Wctrue)

def testObsvSISO(self):
A = np.array([[1., 2.], [3., 4.]])
C = np.array([[5., 7.]])
Expand All @@ -62,6 +70,14 @@ def testObsvMIMO(self):
Wotrue = np.array([[5., 6.], [7., 8.], [23., 34.], [31., 46.]])
Wo = obsv(A, C)
np.testing.assert_array_almost_equal(Wo, Wotrue)

def testObsvT(self):
A = np.array([[1., 2.], [3., 4.]])
C = np.array([[5., 6.], [7., 8.]])
t = 1
Wotrue = np.array([[5., 6.], [7., 8.]])
Wo = obsv(A, C, t=t)
np.testing.assert_array_almost_equal(Wo, Wotrue)

def testCtrbObsvDuality(self):
A = np.array([[1.2, -2.3], [3.4, -4.5]])
Expand Down