diff --git a/.github/workflows/python-package-conda.yml b/.github/workflows/python-package-conda.yml index 0744906a7..87cece16b 100644 --- a/.github/workflows/python-package-conda.yml +++ b/.github/workflows/python-package-conda.yml @@ -4,7 +4,7 @@ on: [push, pull_request] jobs: test-linux: - 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' || '' }} + 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' || '' }}${{ matrix.cvxopt && format(' with cvxopt from {0}', matrix.cvxopt) || ' without cvxopt' }} runs-on: ubuntu-latest strategy: @@ -13,6 +13,7 @@ jobs: python-version: [3.7, 3.9] slycot: ["", "conda"] pandas: [""] + cvxopt: ["", "conda"] array-and-matrix: [0] include: - python-version: 3.9 @@ -45,6 +46,9 @@ jobs: if [[ '${{matrix.pandas}}' == 'conda' ]]; then conda install pandas fi + if [[ '${{matrix.cvxopt}}' == 'conda' ]]; then + conda install -c conda-forge cvxopt + fi - name: Test with pytest env: diff --git a/control/exception.py b/control/exception.py index f66eb7f30..575c78c0a 100644 --- a/control/exception.py +++ b/control/exception.py @@ -84,3 +84,15 @@ def pandas_check(): except: pandas_installed = False return pandas_installed + +# Utility function to see if cvxopt is installed +cvxopt_installed = None +def cvxopt_check(): + global cvxopt_installed + if cvxopt_installed is None: + try: + import cvxopt + cvxopt_installed = True + except: + cvxopt_installed = False + return cvxopt_installed diff --git a/control/lti.py b/control/lti.py index fdb4946cd..b87944cd0 100644 --- a/control/lti.py +++ b/control/lti.py @@ -13,6 +13,7 @@ """ import numpy as np + from numpy import absolute, real, angle, abs from warnings import warn from . import config @@ -21,6 +22,7 @@ __all__ = ['poles', 'zeros', 'damp', 'evalfr', 'frequency_response', 'freqresp', 'dcgain', 'pole', 'zero'] + class LTI(NamedIOSystem): """LTI is a parent class to linear time-invariant (LTI) system objects. @@ -44,6 +46,7 @@ class LTI(NamedIOSystem): Note: dt processing has been moved to the NamedIOSystem class. """ + def __init__(self, inputs=1, outputs=1, states=None, name=None, **kwargs): """Assign the LTI object's numbers of inputs and ouputs.""" super().__init__( @@ -71,8 +74,7 @@ def _set_inputs(self, value): #: Deprecated inputs = property( - _get_inputs, _set_inputs, doc= - """ + _get_inputs, _set_inputs, doc=""" Deprecated attribute; use :attr:`ninputs` instead. The ``inputs`` attribute was used to store the number of system @@ -94,8 +96,7 @@ def _set_outputs(self, value): #: Deprecated outputs = property( - _get_outputs, _set_outputs, doc= - """ + _get_outputs, _set_outputs, doc=""" Deprecated attribute; use :attr:`noutputs` instead. The ``outputs`` attribute was used to store the number of system @@ -201,6 +202,11 @@ def _dcgain(self, warn_infinite): else: return zeroresp + def ispassive(self): + # importing here prevents circular dependancy + from control.passivity import ispassive + return ispassive(self) + # # Deprecated functions # @@ -321,7 +327,7 @@ def damp(sys, doprint=True): wn, damping, poles = sys.damp() if doprint: print('_____Eigenvalue______ Damping___ Frequency_') - for p, d, w in zip(poles, damping, wn) : + for p, d, w in zip(poles, damping, wn): if abs(p.imag) < 1e-12: print("%10.4g %10.4g %10.4g" % (p.real, 1.0, -p.real)) @@ -330,6 +336,7 @@ def damp(sys, doprint=True): (p.real, p.imag, d, w)) return wn, damping, poles + def evalfr(sys, x, squeeze=None): """Evaluate the transfer function of an LTI system for complex frequency x. @@ -388,6 +395,7 @@ def evalfr(sys, x, squeeze=None): """ return sys.__call__(x, squeeze=squeeze) + def frequency_response(sys, omega, squeeze=None): """Frequency response of an LTI system at multiple angular frequencies. diff --git a/control/passivity.py b/control/passivity.py new file mode 100644 index 000000000..e833fbf96 --- /dev/null +++ b/control/passivity.py @@ -0,0 +1,87 @@ +''' +Author: Mark Yeatman +Date: May 15, 2022 +''' + +import numpy as np +from control import statesp as ss + +try: + import cvxopt as cvx +except ImportError as e: + cvx = None + + +def ispassive(sys): + ''' + Indicates if a linear time invariant (LTI) system is passive + + Constructs a linear matrix inequality and a feasibility optimization + such that if a solution exists, the system is passive. + + The source for the algorithm is: + McCourt, Michael J., and Panos J. Antsaklis. + "Demonstrating passivity and dissipativity using computational methods." ISIS 8 (2013). + + Parameters + ---------- + sys: A continuous LTI system + System to be checked. + + Returns + ------- + bool: + The input system passive. + ''' + if cvx is None: + raise ModuleNotFoundError("cvxopt required for passivity module") + + sys = ss._convert_to_statespace(sys) + + A = sys.A + B = sys.B + C = sys.C + D = sys.D + + # account for strictly proper systems + [n, m] = D.shape + D = D + np.nextafter(0, 1)*np.eye(n, m) + + [n, _] = A.shape + A = A - np.nextafter(0, 1)*np.eye(n) + + def make_LMI_matrix(P): + V = np.vstack(( + np.hstack((A.T @ P + P@A, P@B)), + np.hstack((B.T@P, np.zeros_like(D)))) + ) + return V + + matrix_list = [] + state_space_size = sys.nstates + for i in range(0, state_space_size): + for j in range(0, state_space_size): + if j <= i: + P = np.zeros_like(A) + P[i, j] = 1.0 + P[j, i] = 1.0 + matrix_list.append(make_LMI_matrix(P).flatten()) + + coefficents = np.vstack(matrix_list).T + + constants = -np.vstack(( + np.hstack((np.zeros_like(A), - C.T)), + np.hstack((- C, -D - D.T))) + ) + + number_of_opt_vars = int( + (state_space_size**2-state_space_size)/2 + state_space_size) + c = cvx.matrix(0.0, (number_of_opt_vars, 1)) + + # crunch feasibility solution + cvx.solvers.options['show_progress'] = False + sol = cvx.solvers.sdp(c, + Gs=[cvx.matrix(coefficents)], + hs=[cvx.matrix(constants)]) + + return (sol["x"] is not None) diff --git a/control/tests/conftest.py b/control/tests/conftest.py index ac35748f3..1201b8746 100644 --- a/control/tests/conftest.py +++ b/control/tests/conftest.py @@ -17,6 +17,8 @@ # pytest.param(marks=) slycotonly = pytest.mark.skipif(not control.exception.slycot_check(), reason="slycot not installed") +cvxoptonly = pytest.mark.skipif(not control.exception.cvxopt_check(), + reason="cvxopt not installed") matrixfilter = pytest.mark.filterwarnings("ignore:.*matrix subclass:" "PendingDeprecationWarning") matrixerrorfilter = pytest.mark.filterwarnings("error:.*matrix subclass:" diff --git a/control/tests/passivity_test.py b/control/tests/passivity_test.py new file mode 100644 index 000000000..791d70b6c --- /dev/null +++ b/control/tests/passivity_test.py @@ -0,0 +1,74 @@ +''' +Author: Mark Yeatman +Date: May 30, 2022 +''' +import pytest +import numpy +from control import ss, passivity, tf +from control.tests.conftest import cvxoptonly + + +pytestmark = cvxoptonly + + +def test_ispassive(): + A = numpy.array([[0, 1], [-2, -2]]) + B = numpy.array([[0], [1]]) + C = numpy.array([[-1, 2]]) + D = numpy.array([[1.5]]) + sys = ss(A, B, C, D) + + # happy path is passive + assert(passivity.ispassive(sys)) + + # happy path not passive + D = -D + sys = ss(A, B, C, D) + + assert(not passivity.ispassive(sys)) + + +A_d = numpy.array([[-2, 0], [0, 0]]) +A = numpy.array([[-3, 0], [0, -2]]) +B = numpy.array([[0], [1]]) +C = numpy.array([[-1, 2]]) +D = numpy.array([[1.5]]) + + +@pytest.mark.parametrize( + "test_input,expected", + [((A, B, C, D*0.0), True), + ((A_d, B, C, D), True), + ((A*1e12, B, C, D*0), True), + ((A, B*0, C*0, D), True), + ((A*0, B, C, D), True), + ((A*0, B*0, C*0, D*0), True)]) +def test_ispassive_edge_cases(test_input, expected): + + # strictly proper + A = test_input[0] + B = test_input[1] + C = test_input[2] + D = test_input[3] + sys = ss(A, B, C, D) + assert(passivity.ispassive(sys) == expected) + + +def test_transfer_function(): + sys = tf([1], [1, 2]) + assert(passivity.ispassive(sys)) + + sys = tf([1], [1, -2]) + assert(not passivity.ispassive(sys)) + + +def test_oo_style(): + A = numpy.array([[0, 1], [-2, -2]]) + B = numpy.array([[0], [1]]) + C = numpy.array([[-1, 2]]) + D = numpy.array([[1.5]]) + sys = ss(A, B, C, D) + assert(sys.ispassive()) + + sys = tf([1], [1, 2]) + assert(sys.ispassive()) diff --git a/setup.py b/setup.py index df3f8519d..2021d5eb9 100644 --- a/setup.py +++ b/setup.py @@ -46,6 +46,7 @@ 'matplotlib'], extras_require={ 'test': ['pytest', 'pytest-timeout'], - 'slycot': [ 'slycot>=0.4.0' ] + 'slycot': [ 'slycot>=0.4.0' ], + 'cvxopt': [ 'cvxopt>=1.2.0' ] } ) pFad - Phonifier reborn

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