System norms #960

henriks76 · 2024-01-08T13:17:51Z

Hello,

I have written a new function norm to compute H_2 and L_infinity system norms of LTI objects.

Please do let me know if you have any suggested improvements.

Best regards,
Henrik

* Added control/tests/sysnorm_test.py

murrayrm · 2024-01-08T15:27:41Z

@henriks76 It looks like there are some problems when slycot is installed. Can you take a look at the failed unit tests above and see what is going on. From a quick look, there may be an inconsistency in inf and nan that might be something we need to fix elsewhere (but that will be required for your function to work correctly).

control/__init__.py

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

henriks76 · 2024-01-09T16:40:43Z

@henriks76 It looks like there are some problems when slycot is installed. Can you take a look at the failed unit tests above and see what is going on. From a quick look, there may be an inconsistency in inf and nan that might be something we need to fix elsewhere (but that will be required for your function to work correctly).

Thanks @murrayrm . Odd, I have slycot installed but did not get this fault in the tests.

The problem seems to occur when the poles are very close to the stability boundary. I think the poles must first all have been evaluated as being stable, but then the Lyapunov equation is so ill-conditioned that the solution is not positive semi-definite, resulting in a negative number inside np.sqrt giving NaN.

I have added more tests and also warning messages. Let's see if that solves the problem...

bnavigator · 2024-01-09T18:34:08Z

control/tests/sysnorm_test.py

+    s = ct.tf('s')
+    G1 = 1/(s+1)
+    assert np.allclose(ct.norm(G1, p='inf', tol=1e-9), 1.0, rtol=1e-09, atol=1e-08) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(G1, p=2), 0.707106781186547, rtol=1e-09, atol=1e-08) # Comparison to norm computed in MATLAB


I think these tolerances are way too tight. On a non x86_64 system, e.g. 32-bit intel, aarch64, PowerPC or even just a different LAPACK/BLAS implementation can give you differently rounded intermediate and final results.

bnavigator · 2024-01-09T18:36:08Z

control/sysnorm.py

+        gamu = max(1.0, 2.0*gaml)  # Candidate upper bound
+        Ip = np.eye(len(D))    
+
+        while any(np.isclose(la.eigvals(_Hamilton_matrix(gamu)).real, 0.0)):  # Find actual upper bound


Have you considered using SLICOT-Routines (already or to be wrapped by Slycot) optimized for certain Hamiltonian matrices instead of the generic scipy eigenvalue solver? (I didn't check if the SLICOT routines are applicable here)

coveralls · 2024-01-09T18:41:09Z

coverage: 94.431% (-0.4%) from 94.784%
when pulling 14fce67 on henriks76:system-norms
into a8a54d1 on python-control:main.

bnavigator · 2024-01-09T18:47:24Z

control/sysnorm.py

+            poles_real_part = G.poles().real    
+            if any(np.isclose(poles_real_part, 0.0)):
+                if print_warning:
+                    print("Warning: Poles close to, or on, the imaginary axis. Norm value may be uncertain.")


Don't use print here and in the error cases below. For warnings use warnings, if it is an error, please keep raising the exception. And be more specific than just Exception.

KybernetikJo · 2024-01-09T19:46:46Z

FWIW, there also 2 SLICOT / Slycot routines

ab13bd -> H2 or L2 norm of a state space system

ab13bd is part of Slycot 0.5.4, but there was a problem python-control/Slycot#199
It should be fixed in Slycot 0.6.0!

ab13dd -> L-infinity norm of a state space system

ab13dd is already part of python-control, called linfnorm() in
https://github.com/python-control/python-control/blob/main/control/statesp.py
but missing in the sphinx documentation
https://github.com/python-control/python-control/blob/main/doc/control.rst

* Added control/tests/sysnorm_test.py

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

* Use of warnings package. * Use routine statesp.linfnorm when slycot installed. * New routine internal _h2norm_slycot when slycot is installed.

…ntrol into system-norms

henriks76 · 2024-01-21T20:35:58Z

Thanks for the feedback @bnavigator and @KybernetikJo . Incorporated warnings and slycot routines when available now.

KybernetikJo · 2024-01-22T19:33:28Z

control/sysnorm.py

+    >>> ct.norm(Gc,'inf',tol=1e-10)
+    1.0000000000582077
+    """
+    G = ct.ss(system)


You might want to add a type check similar to

if not isinstance(sys, (StateSpace, TransferFunction)): raise TypeError('Parameter ``sys``: must be a ``StateSpace`` or ``TransferFunction``)')

befor calling

G = ct.ss(sys)

KybernetikJo · 2024-01-22T19:50:10Z

control/sysnorm.py

+
+#------------------------------------------------------------------------------
+
+def norm(system, p=2, tol=1e-10, print_warning=True, use_slycot=True):


The optional argument

use_slycot=True

could be replaced by an optional argument

method=None

as in https://github.com/python-control/python-control/blob/main/control/mateqn.py.
Hint: You may want to reuse the following method from mateqn.py:

def _slycot_or_scipy(method): if method == 'slycot' or (method is None and slycot_check()): return 'slycot' elif method == 'scipy' or (method is None and not slycot_check()): return 'scipy' else: raise ControlArgument("Unknown method %s" % method)

The argument method has three options method=[None,"slycot","scipy"] and the following behavior:

If method is None and slycot is installed, then use slycot.

If method is None and slycot is not installed, then fall back on scipy. (Fallback)

If method=="slycot" then try to use slycot or raise an Exception when slycot is not available. (No Fallback)

If method=="scipy" then use scipy. (scipy is always available)

Thanks for the tips. It should be implemented now.

Please don't duplicate code. Reuse it, maybe move it to a common place, but don't repeat yourself (or previous contributors)

Fix examples

* Added control/tests/sysnorm_test.py

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

* Use of warnings package. * Use routine statesp.linfnorm when slycot installed. * New routine internal _h2norm_slycot when slycot is installed.

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

* type check when calling ct.norm * metod argument in ct.norm (slycot or scipy)

…ntrol into system-norms

bnavigator · 2024-01-28T16:55:51Z

examples/type2_type3.py

@@ -5,7 +5,7 @@
 import os
 import matplotlib.pyplot as plt  # Grab MATLAB plotting functions
 from control.matlab import *     # MATLAB-like functions
-from scipy import pi
+from numpy import pi


This has already been resolved in #965. Please rebase.

Ok, I tried again.

Nope.

Fast forward your main branch to upstream/main

In system-norms use git rebase -i main

https://github.com/python-control/python-control/wiki/How-to-contribute-with-a-pull-request

This gets rid of the extra commits which are already in the main branch. While you are at it, you can also squash some of the commits and use better messages than "Update sysnorm.py"

I did steps 7-9:

... `git checkout main; git fetch --all; git merge origin/main
git push
and then bring those changes into your branch:

git checkout ; git rebase main`

Is it step 12 I should do?
git checkout main; git fetch --all; git merge upstream/main

I am afraid your multiple merges and manual fixes like 7a5af50 have created a situation which git cannot resolve automatically:

[ben@skylab:~/src/python-control]% git status [0] On branch system-norms Your branch is up to date with 'henriks76/system-norms'. nothing to commit, working tree clean [ben@skylab:~/src/python-control]% git rebase main [0] Auto-merging control/sysnorm.py CONFLICT (add/add): Merge conflict in control/sysnorm.py error: could not apply fd076c5... New function for LTI system norm computation hint: Resolve all conflicts manually, mark them as resolved with hint: "git add/rm <conflicted_files>", then run "git rebase --continue". hint: You can instead skip this commit: run "git rebase --skip". hint: To abort and get back to the state before "git rebase", run "git rebase --abort". Could not apply fd076c5... New function for LTI system norm computation [ben@skylab:~/src/python-control]% git status [1] interactive rebase in progress; onto 85328d9 Last commands done (10 commands done): pick 49f7e5f Update sysnorm.py pick fd076c5 New function for LTI system norm computation (see more in file .git/rebase-merge/done) Next commands to do (9 remaining commands): pick 0fe2c57 * Updated documentation of function norm * Added control/tests/sysnorm_test.py pick cdf4bab Update sysnorm.py (use "git rebase --edit-todo" to view and edit) You are currently rebasing branch 'system-norms' on '85328d9'. (fix conflicts and then run "git rebase --continue") (use "git rebase --skip" to skip this patch) (use "git rebase --abort" to check out the original branch) Unmerged paths: (use "git restore --staged <file>..." to unstage) (use "git add <file>..." to mark resolution) both added: control/sysnorm.py no changes added to commit (use "git add" and/or "git commit -a")

You have to go through it step by step, because only you know what is relevant.

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

…ntrol into system-norms

bnavigator · 2024-01-28T21:38:47Z

@henriks76, you can use https://github.com/bnavigator/python-control/tree/system-norms2 and re-open if you want. I basically picked the relevant commits in order, without the merge and duplication stuff.

bnavigator · 2024-01-28T21:42:50Z

Or do git rebase -i main and use this picklist:

pick 7ace4bc New function for LTI system norm computation
pick 5103448 * Updated documentation of function norm * Added control/tests/sysnorm_test.py
pick 4fb252e Update sysnorm.py
pick 108817c Do not track changes in VS Code setup.
pick 6683eb3 Lowered tolerances in tests.
pick 32d38bf Added: * Use of warnings package. * Use routine statesp.linfnorm when slycot installed. * New routine internal _h2norm_slycot when slycot is installed.
pick 793f0d6 Added: * type check when calling ct.norm * metod argument in ct.norm (slycot or scipy)
pick fe22e33 Use function _slycot_or_scipy from ct.mateqn

# Rebase 85328d9..fe22e33 onto 85328d9 (20 commands)
#
# Commands:
# p, pick <commit> = use commit
# r, reword <commit> = use commit, but edit the commit message
# e, edit <commit> = use commit, but stop for amending
# s, squash <commit> = use commit, but meld into previous commit
# f, fixup [-C | -c] <commit> = like "squash" but keep only the previous
#                    commit's log message, unless -C is used, in which case
#                    keep only this commit's message; -c is same as -C but
#                    opens the editor
# x, exec <command> = run command (the rest of the line) using shell
# b, break = stop here (continue rebase later with 'git rebase --continue')
# d, drop <commit> = remove commit
# l, label <label> = label current HEAD with a name
# t, reset <label> = reset HEAD to a label
# m, merge [-C <commit> | -c <commit>] <label> [# <oneline>]
#         create a merge commit using the original merge commit's
#         message (or the oneline, if no original merge commit was
#         specified); use -c <commit> to reword the commit message
# u, update-ref <ref> = track a placeholder for the <ref> to be updated
#                       to this position in the new commits. The <ref> is
#                       updated at the end of the rebase
#
# These lines can be re-ordered; they are executed from top to bottom.
#
# If you remove a line here THAT COMMIT WILL BE LOST.
#
# However, if you remove everything, the rebase will be aborted.
#

henriks76 · 2024-02-04T12:11:39Z

Or do git rebase -i main and use this picklist:

pick 7ace4bc New function for LTI system norm computation
pick 5103448 * Updated documentation of function norm * Added control/tests/sysnorm_test.py
pick 4fb252e Update sysnorm.py
pick 108817c Do not track changes in VS Code setup.
pick 6683eb3 Lowered tolerances in tests.
pick 32d38bf Added: * Use of warnings package. * Use routine statesp.linfnorm when slycot installed. * New routine internal _h2norm_slycot when slycot is installed.
pick 793f0d6 Added: * type check when calling ct.norm * metod argument in ct.norm (slycot or scipy)
pick fe22e33 Use function _slycot_or_scipy from ct.mateqn

# Rebase 85328d9..fe22e33 onto 85328d9 (20 commands)
#
# Commands:
# p, pick <commit> = use commit
# r, reword <commit> = use commit, but edit the commit message
# e, edit <commit> = use commit, but stop for amending
# s, squash <commit> = use commit, but meld into previous commit
# f, fixup [-C | -c] <commit> = like "squash" but keep only the previous
#                    commit's log message, unless -C is used, in which case
#                    keep only this commit's message; -c is same as -C but
#                    opens the editor
# x, exec <command> = run command (the rest of the line) using shell
# b, break = stop here (continue rebase later with 'git rebase --continue')
# d, drop <commit> = remove commit
# l, label <label> = label current HEAD with a name
# t, reset <label> = reset HEAD to a label
# m, merge [-C <commit> | -c <commit>] <label> [# <oneline>]
#         create a merge commit using the original merge commit's
#         message (or the oneline, if no original merge commit was
#         specified); use -c <commit> to reword the commit message
# u, update-ref <ref> = track a placeholder for the <ref> to be updated
#                       to this position in the new commits. The <ref> is
#                       updated at the end of the rebase
#
# These lines can be re-ordered; they are executed from top to bottom.
#
# If you remove a line here THAT COMMIT WILL BE LOST.
#
# However, if you remove everything, the rebase will be aborted.
#

Thanks @bnavigator, this was very helpful! I squashed some commits in https://github.com/henriks76/python-control as well. Or is it better to continue on https://github.com/bnavigator/python-control/tree/system-norms2 ?

bnavigator · 2024-02-04T12:22:13Z

Both would be fine.

Note:

ben@skylab:~/src/python-control> git status
On branch system-norms
Your branch is up to date with 'henriks76/system-norms'.

nothing to commit, working tree clean
ben@skylab:~/src/python-control> git diff system-norms2

diff --git a/control/tests/sysnorm_test.py b/control/tests/sysnorm_test.py
index 917e98d..74e8de0 100644
--- a/control/tests/sysnorm_test.py
+++ b/control/tests/sysnorm_test.py
@@ -13,35 +13,35 @@ def test_norm_1st_order_stable_system():
     """First-order stable continuous-time system"""
     s = ct.tf('s')
     G1 = 1/(s+1)
-    assert np.allclose(ct.norm(G1, p='inf', tol=1e-9), 1.0) # Comparison to norm computed in MATLAB
-    assert np.allclose(ct.norm(G1, p=2), 0.707106781186547) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(G1, p='inf', tol=1e-9, print_warning=False), 1.0) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(G1, p=2, print_warning=False), 0.707106781186547) # Comparison to norm computed in MATLAB
     
     Gd1 = ct.sample_system(G1, 0.1)
-    assert np.allclose(ct.norm(Gd1, p='inf', tol=1e-9), 1.0) # Comparison to norm computed in MATLAB
-    assert np.allclose(ct.norm(Gd1, p=2), 0.223513699524858) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(Gd1, p='inf', tol=1e-9, print_warning=False), 1.0) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(Gd1, p=2, print_warning=False), 0.223513699524858) # Comparison to norm computed in MATLAB
 
 
 def test_norm_1st_order_unstable_system():
     """First-order unstable continuous-time system"""
     s = ct.tf('s')
     G2 = 1/(1-s)
-    assert np.allclose(ct.norm(G2, p='inf', tol=1e-9), 1.0) # Comparison to norm computed in MATLAB
-    assert ct.norm(G2, p=2) == float('inf') # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(G2, p='inf', tol=1e-9, print_warning=False), 1.0) # Comparison to norm computed in MATLAB
+    assert ct.norm(G2, p=2, print_warning=False) == float('inf') # Comparison to norm computed in MATLAB
     
     Gd2 = ct.sample_system(G2, 0.1)
-    assert np.allclose(ct.norm(Gd2, p='inf', tol=1e-9), 1.0) # Comparison to norm computed in MATLAB
-    assert ct.norm(Gd2, p=2) == float('inf') # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(Gd2, p='inf', tol=1e-9, print_warning=False), 1.0) # Comparison to norm computed in MATLAB
+    assert ct.norm(Gd2, p=2, print_warning=False) == float('inf') # Comparison to norm computed in MATLAB
 
 def test_norm_2nd_order_system_imag_poles():
     """Second-order continuous-time system with poles on imaginary axis"""
     s = ct.tf('s')
     G3 = 1/(s**2+1)
-    assert ct.norm(G3, p='inf') == float('inf') # Comparison to norm computed in MATLAB
-    assert ct.norm(G3, p=2) == float('inf') # Comparison to norm computed in MATLAB
+    assert ct.norm(G3, p='inf', print_warning=False) == float('inf') # Comparison to norm computed in MATLAB
+    assert ct.norm(G3, p=2, print_warning=False) == float('inf') # Comparison to norm computed in MATLAB
     
     Gd3 = ct.sample_system(G3, 0.1)
-    assert ct.norm(Gd3, p='inf') == float('inf') # Comparison to norm computed in MATLAB
-    assert ct.norm(Gd3, p=2) == float('inf') # Comparison to norm computed in MATLAB
+    assert ct.norm(Gd3, p='inf', print_warning=False) == float('inf') # Comparison to norm computed in MATLAB
+    assert ct.norm(Gd3, p=2, print_warning=False) == float('inf') # Comparison to norm computed in MATLAB
 
 def test_norm_3rd_order_mimo_system():
     """Third-order stable MIMO continuous-time system"""
@@ -55,9 +55,9 @@ def test_norm_3rd_order_mimo_system():
                   [-0.863652821988714,  -1.214117043615409,  -0.006849328103348]])
     D = np.zeros((2,2))
     G4 = ct.ss(A,B,C,D) # Random system generated in MATLAB
-    assert np.allclose(ct.norm(G4, p='inf', tol=1e-9), 4.276759162964244) # Comparison to norm computed in MATLAB
-    assert np.allclose(ct.norm(G4, p=2), 2.237461821810309) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(G4, p='inf', tol=1e-9, print_warning=False), 4.276759162964244) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(G4, p=2, print_warning=False), 2.237461821810309) # Comparison to norm computed in MATLAB
     
     Gd4 = ct.sample_system(G4, 0.1)
-    assert np.allclose(ct.norm(Gd4, p='inf', tol=1e-9), 4.276759162964228) # Comparison to norm computed in MATLAB
-    assert np.allclose(ct.norm(Gd4, p=2), 0.707434962289554) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(Gd4, p='inf', tol=1e-9, print_warning=False), 4.276759162964228) # Comparison to norm computed in MATLAB
+    assert np.allclose(ct.norm(Gd4, p=2, print_warning=False), 0.707434962289554) # Comparison to norm computed in MATLAB

henriks76 · 2024-02-04T12:33:12Z

Yes, I stopped the printout of warnings to not clutter the output of pytest. If it is better to put it back in I can do it, of course.

bnavigator · 2024-02-04T12:35:23Z

Remind me, what was the warning about, again?

henriks76 · 2024-02-04T12:40:53Z

warnings.warn("System has a direct feedthrough term!")
warnings.warn("System has pole(s) on the stability boundary!")
warnings.warn("System has a direct feedthrough term!")
warnings.warn("System is unstable!")
warnings.warn("Poles close to, or on, the imaginary axis. Norm value may be uncertain.")

Many of the tests gave these warnings.

bnavigator · 2024-02-04T12:49:47Z

I'd prefer to use a pytest.warns context manager or the recwarn fixture for this, if possible.

henriks76 · 2024-02-11T12:38:23Z

Thanks @bnavigator, I now use a pytest.warns context manager instead.

bnavigator · 2024-02-18T11:44:37Z

Continued in #971

Henrik Sandberg added 2 commits January 8, 2024 09:43

New function for LTI system norm computation

6a0e136

* Updated documentation of function norm

a0fbc80

* Added control/tests/sysnorm_test.py

bnavigator reviewed Jan 8, 2024

View reviewed changes

control/__init__.py Show resolved Hide resolved

Update sysnorm.py

457c623

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

bnavigator reviewed Jan 9, 2024

View reviewed changes

henriks76 and others added 8 commits January 21, 2024 19:13

Merge branch 'python-control:main' into system-norms

adcb486

New function for LTI system norm computation

fd076c5

* Updated documentation of function norm

0fe2c57

* Added control/tests/sysnorm_test.py

Update sysnorm.py

cdf4bab

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

Do not track changes in VS Code setup.

34f9537

Lowered tolerances in tests.

b419f12

Added:

9ecd594

* Use of warnings package. * Use routine statesp.linfnorm when slycot installed. * New routine internal _h2norm_slycot when slycot is installed.

Merge branch 'system-norms' of https://github.com/henriks76/python-co…

14fce67

…ntrol into system-norms

bnavigator added 2 commits January 22, 2024 20:54

escape latex labels

5c38d4f

Use Numpy API for pi instead of undocumented scipy.pi

99e56f8

KybernetikJo reviewed Jan 22, 2024

View reviewed changes

bnavigator and others added 7 commits January 22, 2024 21:52

Update notebooks (no rerun, no output change)

2c32913

Merge pull request python-control#965 from bnavigator/fix-examples

85328d9

Fix examples

New function for LTI system norm computation

7ace4bc

* Updated documentation of function norm

5103448

* Added control/tests/sysnorm_test.py

Update sysnorm.py

4fb252e

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

Do not track changes in VS Code setup.

108817c

Lowered tolerances in tests.

6683eb3

Henrik Sandberg added 5 commits January 28, 2024 16:05

Added:

32d38bf

* Use of warnings package. * Use routine statesp.linfnorm when slycot installed. * New routine internal _h2norm_slycot when slycot is installed.

Update sysnorm.py

6f810ba

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

Added:

793f0d6

* type check when calling ct.norm * metod argument in ct.norm (slycot or scipy)

Merge branch 'system-norms' of https://github.com/henriks76/python-co…

12ba677

…ntrol into system-norms

Fixed merge error with __all__.

7a5af50

bnavigator reviewed Jan 28, 2024

View reviewed changes

Henrik Sandberg added 2 commits January 28, 2024 18:30

Update sysnorm.py

49f7e5f

* Added additional tests and warning messages for systems with poles close to stability boundary * Added __all__ * Added more comments

Merge branch 'system-norms' of https://github.com/henriks76/python-co…

247cff5

…ntrol into system-norms

henriks76 closed this Jan 28, 2024

bnavigator mentioned this pull request Feb 18, 2024

System norms 2 #971

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		#------------------------------------------------------------------------------

		def norm(system, p=2, tol=1e-10, print_warning=True, use_slycot=True):

System norms #960

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bnavigator commented Jan 28, 2024

bnavigator commented Jan 28, 2024

henriks76 commented Feb 4, 2024

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coveralls commented Jan 9, 2024 •

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bnavigator commented Feb 4, 2024 •

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