def test_linear_affine_system(self):
# Just make sure linear system is spelled correctly.
A = np.identity(2)
B = np.array([[0], [1]])
f0 = np.array([[0], [0]])
C = np.array([[0, 1]])
D = [0]
y0 = [0]
system = LinearSystem(A, B, C, D)
context = system.CreateDefaultContext()
self.assertEqual(system.get_input_port(0).size(), 1)
self.assertEqual(context.get_mutable_continuous_state_vector().size(),
2)
self.assertEqual(system.get_output_port(0).size(), 1)
self.assertTrue((system.A() == A).all())
self.assertTrue((system.B() == B).all())
self.assertTrue((system.f0() == f0).all())
self.assertTrue((system.C() == C).all())
self.assertEqual(system.D(), D)
self.assertEqual(system.y0(), y0)
self.assertEqual(system.time_period(), 0.)
Co = ControllabilityMatrix(system)
self.assertEqual(Co.shape, (2, 2))
self.assertFalse(IsControllable(system))
self.assertFalse(IsControllable(system, 1e-6))
Ob = ObservabilityMatrix(system)
self.assertEqual(Ob.shape, (2, 2))
self.assertFalse(IsObservable(system))
system = AffineSystem(A, B, f0, C, D, y0, .1)
self.assertEqual(system.get_input_port(0), system.get_input_port())
self.assertEqual(system.get_output_port(0), system.get_output_port())
context = system.CreateDefaultContext()
self.assertEqual(system.get_input_port(0).size(), 1)
self.assertEqual(context.get_discrete_state_vector().size(), 2)
self.assertEqual(system.get_output_port(0).size(), 1)
self.assertTrue((system.A() == A).all())
self.assertTrue((system.B() == B).all())
self.assertTrue((system.f0() == f0).all())
self.assertTrue((system.C() == C).all())
self.assertEqual(system.D(), D)
self.assertEqual(system.y0(), y0)
self.assertEqual(system.time_period(), .1)
system.get_input_port(0).FixValue(context, 0)
linearized = Linearize(system, context)
self.assertTrue((linearized.A() == A).all())
taylor = FirstOrderTaylorApproximation(system, context)
self.assertTrue((taylor.y0() == y0).all())
system = MatrixGain(D=A)
self.assertTrue((system.D() == A).all())
def test_linear_affine_system(self):
# Just make sure linear system is spelled correctly.
A = np.identity(2)
B = np.array([[0], [1]])
f0 = np.array([[0], [0]])
C = np.array([[0, 1]])
D = [0]
y0 = [0]
system = LinearSystem(A, B, C, D)
context = system.CreateDefaultContext()
self.assertEqual(system.get_input_port(0).size(), 1)
self.assertEqual(context.get_mutable_continuous_state_vector().size(),
2)
self.assertEqual(system.get_output_port(0).size(), 1)
self.assertTrue((system.A() == A).all())
self.assertTrue((system.B() == B).all())
self.assertTrue((system.f0() == f0).all())
self.assertTrue((system.C() == C).all())
self.assertEqual(system.D(), D)
self.assertEqual(system.y0(), y0)
self.assertEqual(system.time_period(), 0.)
x0 = np.array([1, 2])
system.configure_default_state(x0=x0)
system.SetDefaultContext(context)
np.testing.assert_equal(
context.get_continuous_state_vector().CopyToVector(), x0)
generator = RandomGenerator()
system.SetRandomContext(context, generator)
np.testing.assert_equal(
context.get_continuous_state_vector().CopyToVector(), x0)
system.configure_random_state(covariance=np.eye(2))
system.SetRandomContext(context, generator)
self.assertNotEqual(
context.get_continuous_state_vector().CopyToVector()[1], x0[1])
Co = ControllabilityMatrix(system)
self.assertEqual(Co.shape, (2, 2))
self.assertFalse(IsControllable(system))
self.assertFalse(IsControllable(system, 1e-6))
Ob = ObservabilityMatrix(system)
self.assertEqual(Ob.shape, (2, 2))
self.assertFalse(IsObservable(system))
system = AffineSystem(A, B, f0, C, D, y0, .1)
self.assertEqual(system.get_input_port(0), system.get_input_port())
self.assertEqual(system.get_output_port(0), system.get_output_port())
context = system.CreateDefaultContext()
self.assertEqual(system.get_input_port(0).size(), 1)
self.assertEqual(context.get_discrete_state_vector().size(), 2)
self.assertEqual(system.get_output_port(0).size(), 1)
self.assertTrue((system.A() == A).all())
self.assertTrue((system.B() == B).all())
self.assertTrue((system.f0() == f0).all())
self.assertTrue((system.C() == C).all())
self.assertEqual(system.D(), D)
self.assertEqual(system.y0(), y0)
self.assertEqual(system.time_period(), .1)
system.get_input_port(0).FixValue(context, 0)
linearized = Linearize(system, context)
self.assertTrue((linearized.A() == A).all())
taylor = FirstOrderTaylorApproximation(system, context)
self.assertTrue((taylor.y0() == y0).all())
system = MatrixGain(D=A)
self.assertTrue((system.D() == A).all())
system = TrajectoryAffineSystem(PiecewisePolynomial(A),
PiecewisePolynomial(B),
PiecewisePolynomial(f0),
PiecewisePolynomial(C),
PiecewisePolynomial(D),
PiecewisePolynomial(y0), .1)
self.assertEqual(system.get_input_port(0), system.get_input_port())
self.assertEqual(system.get_output_port(0), system.get_output_port())
context = system.CreateDefaultContext()
self.assertEqual(system.get_input_port(0).size(), 1)
self.assertEqual(context.get_discrete_state_vector().size(), 2)
self.assertEqual(system.get_output_port(0).size(), 1)
for t in np.linspace(0., 1., 5):
self.assertTrue((system.A(t) == A).all())
self.assertTrue((system.B(t) == B).all())
self.assertTrue((system.f0(t) == f0).all())
self.assertTrue((system.C(t) == C).all())
self.assertEqual(system.D(t), D)
self.assertEqual(system.y0(t), y0)
self.assertEqual(system.time_period(), .1)
x0 = np.array([1, 2])
system.configure_default_state(x0=x0)
system.SetDefaultContext(context)
np.testing.assert_equal(
context.get_discrete_state_vector().CopyToVector(), x0)
generator = RandomGenerator()
system.SetRandomContext(context, generator)
np.testing.assert_equal(
context.get_discrete_state_vector().CopyToVector(), x0)
system.configure_random_state(covariance=np.eye(2))
system.SetRandomContext(context, generator)
self.assertNotEqual(
context.get_discrete_state_vector().CopyToVector()[1], x0[1])
system = TrajectoryLinearSystem(A=PiecewisePolynomial(A),
B=PiecewisePolynomial(B),
C=PiecewisePolynomial(C),
D=PiecewisePolynomial(D),
time_period=0.1)
self.assertEqual(system.time_period(), .1)
system.configure_default_state(x0=np.array([1, 2]))
system.configure_random_state(covariance=np.eye(2))