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Added option for computing anti-stabilizing solutions of Riccati equations#281

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Merged
murrayrm merged 6 commits intopython-control:masterfromdbankmann:master
Apr 7, 2019
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7 changes: 5 additions & 2 deletions.travis.yml
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Original file line numberDiff line numberDiff line change
Expand Up@@ -51,8 +51,10 @@ before_install:
- conda create -q -n test-environment python="$TRAVIS_PYTHON_VERSION" pip coverage
- source activate test-environment
# Install openblas if slycot is being used
# also install scikit-build for the build process
- if [[ "$SLYCOT" != "" ]]; then
conda install openblas;
conda install openblas;
conda install -c conda-forge scikit-build;
fi
# Make sure to look in the right place for python libraries (for slycot)
- export LIBRARY_PATH="$HOME/miniconda/envs/test-environment/lib"
Expand All@@ -65,10 +67,11 @@ install:
- conda install $SCIPY matplotlib
# Build slycot from source
# For python 3, need to provide pointer to python library
# Use "Unix Makefiles" as generator, because Ninja cannot handle Fortran
#! git clone https://github.com/repagh/Slycot.git slycot;
- if [[ "$SLYCOT" != "" ]]; then
git clone https://github.com/python-control/Slycot.git slycot;
cd slycot; python setup.py install; cd ..;
cd slycot; python setup.py install -G "Unix Makefiles"; cd ..;
fi

# command to run tests
Expand Down
39 changes: 28 additions & 11 deletionscontrol/mateqn.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -411,7 +411,7 @@ def dlyap(A,Q,C=None,E=None):

#### Riccati equation solvers care and dare

def care(A,B,Q,R=None,S=None,E=None):
def care(A, B, Q,R=None,S=None,E=None, stabilizing=True):
""" (X,L,G) = care(A,B,Q,R=None) solves the continuous-time algebraic Riccati
equation

Expand DownExpand Up@@ -527,7 +527,11 @@ def care(A,B,Q,R=None,S=None,E=None):
raise e

try:
X,rcond,w,S_o,U,A_inv = sb02md(n,A,G,Q,'C')
if stabilizing:
sort = 'S'
else:
sort = 'U'
X, rcond, w, S_o, U, A_inv = sb02md(n, A, G, Q, 'C', sort=sort)
except ValueError as ve:
if ve.info < 0 or ve.info > 5:
e = ValueError(ve.message)
Expand DownExpand Up@@ -613,8 +617,12 @@ def care(A,B,Q,R=None,S=None,E=None):
# Solve the generalized algebraic Riccati equation by calling the
# Slycot function sg02ad
try:
rcondu,X,alfar,alfai,beta,S_o,T,U,iwarn = \
sg02ad('C','B','N','U','N','N','S','R',n,m,0,A,E,B,Q,R,S)
if stabilizing:
sort = 'S'
else:
sort = 'U'
rcondu, X, alfar, alfai, beta, S_o, T, U, iwarn = \
sg02ad('C', 'B', 'N', 'U', 'N', 'N', sort, 'R', n, m, 0, A, E, B, Q, R, S)
except ValueError as ve:
if ve.info < 0 or ve.info > 7:
e = ValueError(ve.message)
Expand DownExpand Up@@ -671,7 +679,7 @@ def care(A,B,Q,R=None,S=None,E=None):
else:
raise ControlArgument("Invalid set of input parameters.")

def dare(A,B,Q,R,S=None,E=None):
def dare(A, B, Q, R,S=None,E=None, stabilizing=True):
""" (X,L,G) = dare(A,B,Q,R) solves the discrete-time algebraic Riccati
equation

Expand All@@ -692,8 +700,8 @@ def dare(A,B,Q,R,S=None,E=None):
matrix :math:`G = (B^T X B + R)^{-1} (B^T X A + S^T)` and the closed loop
eigenvalues L, i.e., the eigenvalues of A - B G , E.
"""
if S is not None or E is not None:
return dare_old(A, B, Q, R, S, E)
if S is not None or E is not None or not stabilizing:
return dare_old(A, B, Q, R, S, E, stabilizing)
else:
Rmat = asmatrix(R)
Qmat = asmatrix(Q)
Expand All@@ -702,7 +710,7 @@ def dare(A,B,Q,R,S=None,E=None):
L = eigvals(A - B.dot(G))
return X, L, G

def dare_old(A,B,Q,R,S=None,E=None):
def dare_old(A, B, Q, R,S=None,E=None, stabilizing=True):
# Make sure we can import required slycot routine
try:
from slycot import sb02md
Expand DownExpand Up@@ -795,7 +803,12 @@ def dare_old(A,B,Q,R,S=None,E=None):
raise e

try:
X,rcond,w,S,U,A_inv = sb02md(n,A,G,Q,'D')
if stabilizing:
sort = 'S'
else:
sort = 'U'

X, rcond, w, S, U, A_inv = sb02md(n, A, G, Q, 'D', sort=sort)
except ValueError as ve:
if ve.info < 0 or ve.info > 5:
e = ValueError(ve.message)
Expand DownExpand Up@@ -884,8 +897,12 @@ def dare_old(A,B,Q,R,S=None,E=None):
# Solve the generalized algebraic Riccati equation by calling the
# Slycot function sg02ad
try:
rcondu,X,alfar,alfai,beta,S_o,T,U,iwarn = \
sg02ad('D','B','N','U','N','N','S','R',n,m,0,A,E,B,Q,R,S)
if stabilizing:
sort = 'S'
else:
sort = 'U'
rcondu, X, alfar, alfai, beta, S_o, T, U, iwarn = \
sg02ad('D', 'B', 'N', 'U', 'N', 'N', sort, 'R', n, m, 0, A, E, B, Q, R, S)
except ValueError as ve:
if ve.info < 0 or ve.info > 7:
e = ValueError(ve.message)
Expand Down
32 changes: 32 additions & 0 deletionscontrol/tests/statefbk_test.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -9,6 +9,7 @@
from control.statefbk import ctrb, obsv, place, place_varga, lqr, gram, acker
from control.matlab import *
from control.exception import slycot_check, ControlDimension
from control.mateqn import care, dare

class TestStatefbk(unittest.TestCase):
"""Test state feedback functions"""
Expand DownExpand Up@@ -298,6 +299,37 @@ def test_LQR_3args(self):
K, S, poles = lqr(sys, Q, R)
self.check_LQR(K, S, poles, Q, R)

@unittest.skipIf(not slycot_check(), "slycot not installed")
def test_care(self):
#unit test for stabilizing and anti-stabilizing feedbacks
#continuous-time

A = np.diag([1,-1])
B = np.identity(2)
Q = np.identity(2)
R = np.identity(2)
S = 0 * B
E = np.identity(2)
X, L , G = care(A, B, Q, R, S, E, stabilizing=True)
assert np.all(np.real(L) < 0)
X, L , G = care(A, B, Q, R, S, E, stabilizing=False)
assert np.all(np.real(L) > 0)

@unittest.skipIf(not slycot_check(), "slycot not installed")
def test_dare(self):
#discrete-time
A = np.diag([0.5,2])
B = np.identity(2)
Q = np.identity(2)
R = np.identity(2)
S = 0 * B
E = np.identity(2)
X, L , G = dare(A, B, Q, R, S, E, stabilizing=True)
assert np.all(np.abs(L) < 1)
X, L , G = dare(A, B, Q, R, S, E, stabilizing=False)
assert np.all(np.abs(L) > 1)


def test_suite():
return unittest.TestLoader().loadTestsFromTestCase(TestStatefbk)

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