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Merged
gabrielfrasantos merged 1 commit into from
Aug 8, 2026
Merged

feat: improve nonlinear control algorithms #242

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99 changes: 99 additions & 0 deletions numerical/nonlinear_control/test/TestBacksteppingControl.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -362,3 +362,102 @@ TEST_F(TestBacksteppingRealPlantOrder2, stabilizes_double_integrator)
EXPECT_NEAR(x[0], 0.0f, 1.0e-2f);
EXPECT_NEAR(x[1], 0.0f, 1.0e-2f);
}

TEST_F(TestBacksteppingRealPlantOrder1, reset_restores_initial_response_order1)
{
std::array<float, 1> x{ { 0.8f } };
nonlinear_control::BacksteppingControl<float, 1>::Reference ref{ 0.0f, 0.0f };

const float first = controller.ComputeControl(x, ref);

std::array<float, 1> xOther{ { 2.0f } };
controller.ComputeControl(xOther, ref);
controller.Reset();

const float afterReset = controller.ComputeControl(x, ref);

EXPECT_NEAR(afterReset, first, math::Tolerance<float>());
}

TEST_F(TestBacksteppingControlOrder1, zero_error_output_equals_negative_drift_over_gain)
{
const float d{ 1.2f };
const float g{ 2.0f };
std::array<float, 1> x{ { 0.5f } };
nonlinear_control::BacksteppingControl<float, 1>::Reference ref{ 0.5f, 0.0f };

EXPECT_CALL(model, Drift(0, x)).WillOnce(::testing::Return(d));
EXPECT_CALL(model, Gain(0, x)).WillOnce(::testing::Return(g));

const float u = controller.ComputeControl(x, ref);

EXPECT_NEAR(u, -d / g, math::Tolerance<float>());
}

TEST_F(TestBacksteppingControlOrder1, drift_and_error_combined_output)
{
const float e{ 0.6f };
const float d{ 1.0f };
const float g{ 2.5f };
std::array<float, 1> x{ { e } };
nonlinear_control::BacksteppingControl<float, 1>::Reference ref{ 0.0f, 0.0f };

EXPECT_CALL(model, Drift(0, x)).WillOnce(::testing::Return(d));
EXPECT_CALL(model, Gain(0, x)).WillOnce(::testing::Return(g));

const float u = controller.ComputeControl(x, ref);

EXPECT_NEAR(u, (-d - gains[0] * e) / g, math::Tolerance<float>());
}

TEST_F(TestBacksteppingControlOrder1, two_instances_do_not_share_state)
{
::testing::StrictMock<MockStrictFeedbackModel<float, 1>> modelB;
std::array<float, 1> gainsB{ { 2.0f } };
nonlinear_control::BacksteppingControl<float, 1> ctrlB{ modelB, gainsB };

std::array<float, 1> xA{ { 1.0f } };
std::array<float, 1> xB{ { 1.0f } };
nonlinear_control::BacksteppingControl<float, 1>::Reference ref{ 0.0f, 0.0f };

EXPECT_CALL(model, Drift(0, xA)).WillOnce(::testing::Return(0.0f));
EXPECT_CALL(model, Gain(0, xA)).WillOnce(::testing::Return(1.0f));
EXPECT_CALL(modelB, Drift(0, xB)).WillOnce(::testing::Return(0.0f));
EXPECT_CALL(modelB, Gain(0, xB)).WillOnce(::testing::Return(1.0f));

const float uA = controller.ComputeControl(xA, ref);
const float uB = ctrlB.ComputeControl(xB, ref);

EXPECT_FLOAT_EQ(uA, uB);
}

TEST_F(TestBacksteppingControlOrder1, large_state_produces_finite_output)
{
const float large{ 1.0e6f };
std::array<float, 1> x{ { large } };
nonlinear_control::BacksteppingControl<float, 1>::Reference ref{ 0.0f, 0.0f };

EXPECT_CALL(model, Drift(0, x)).WillOnce(::testing::Return(0.0f));
EXPECT_CALL(model, Gain(0, x)).WillOnce(::testing::Return(1.0f));

const float u = controller.ComputeControl(x, ref);

EXPECT_TRUE(std::isfinite(u));
EXPECT_NEAR(u, -gains[0] * large, 1.0f);
}

TEST_F(TestBacksteppingControlOrder1, determinism_same_input_same_output)
{
std::array<float, 1> x{ { 0.7f } };
nonlinear_control::BacksteppingControl<float, 1>::Reference ref{ 0.2f, 0.1f };

EXPECT_CALL(model, Drift(0, x)).Times(2).WillRepeatedly(::testing::Return(0.3f));
EXPECT_CALL(model, Gain(0, x)).Times(2).WillRepeatedly(::testing::Return(1.5f));

controller.Reset();
const float u1 = controller.ComputeControl(x, ref);
controller.Reset();
const float u2 = controller.ComputeControl(x, ref);

EXPECT_FLOAT_EQ(u1, u2);
}
60 changes: 53 additions & 7 deletions numerical/nonlinear_control/test/TestFeedbackLinearization.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -203,19 +203,65 @@ TEST_F(TestFeedbackLinearization, closed_loop_error_decays)
EXPECT_LT(finalNorm, prevErrorNorm);
}

TEST_F(TestFeedbackLinearization, reference_feedforward_used)
TEST_F(TestFeedbackLinearization, superposition_all_terms_active)
{
const math::SquareMatrix<float, 2> identity{ math::SquareMatrix<float, 2>::Identity() };
const math::SquareMatrix<float, 2> B{ 2.0f, 1.0f, 0.5f, 3.0f };
const math::Vector<float, 2> drift{ { 4.0f }, { -1.0f } };
const math::Vector<float, 2> x{ { 1.0f }, { -1.0f } };
const math::Vector<float, 2> xDot{ { 0.5f }, { 0.25f } };
const math::Vector<float, 2> yd{ { 3.0f }, { 1.0f } };
const math::Vector<float, 2> ydDot{ { 1.5f }, { -0.5f } };
const math::Vector<float, 2> ydDdot{ { 0.2f }, { -0.3f } };

EXPECT_CALL(model, DecouplingMatrixAt(::testing::_)).WillOnce(::testing::Return(B));
EXPECT_CALL(model, DriftTerm(::testing::_)).WillOnce(::testing::Return(drift));

const auto u{ controller.ComputeInput(x, xDot, yd, ydDot, ydDdot) };

const math::Vector<float, 2> e{ yd - x };
const math::Vector<float, 2> eDot{ ydDot - xDot };
const math::Vector<float, 2> v{ ydDdot + kd * eDot + kp * e };
const math::Vector<float, 2> expected{ B * v + drift };

EXPECT_NEAR(u.at(0, 0), expected.at(0, 0), math::Tolerance<float>());
EXPECT_NEAR(u.at(1, 0), expected.at(1, 0), math::Tolerance<float>());
}

TEST_F(TestFeedbackLinearization, off_diagonal_decoupling_matrix_couples_axes)
{
const math::SquareMatrix<float, 2> B{ 0.0f, 1.0f, 1.0f, 0.0f };
const math::Vector<float, 2> a{ { 0.0f }, { 0.0f } };
const math::Vector<float, 2> c{ { 7.0f }, { -4.0f } };
const math::Vector<float, 2> v{ { 5.0f }, { 7.0f } };

EXPECT_CALL(model, DecouplingMatrixAt(::testing::_)).WillOnce(::testing::Return(identity));
EXPECT_CALL(model, DecouplingMatrixAt(::testing::_)).WillOnce(::testing::Return(B));
EXPECT_CALL(model, DriftTerm(::testing::_)).WillOnce(::testing::Return(a));

const auto u{ controller.ComputeInput(zero, zero, zero, zero, c) };
const auto u{ controller.ComputeInput(zero, zero, zero, zero, v) };

EXPECT_NEAR(u.at(0, 0), c.at(0, 0), math::Tolerance<float>());
EXPECT_NEAR(u.at(1, 0), c.at(1, 0), math::Tolerance<float>());
EXPECT_NEAR(u.at(0, 0), 7.0f, math::Tolerance<float>());
EXPECT_NEAR(u.at(1, 0), 5.0f, math::Tolerance<float>());
}

TEST_F(TestFeedbackLinearization, model_queried_with_exact_state)
{
const math::SquareMatrix<float, 2> identity{ math::SquareMatrix<float, 2>::Identity() };
const math::Vector<float, 2> a{ { 0.0f }, { 0.0f } };
const math::Vector<float, 2> xQuery{ { 2.5f }, { -3.1f } };

math::Vector<float, 2> capturedB{};
math::Vector<float, 2> capturedA{};

EXPECT_CALL(model, DecouplingMatrixAt(::testing::_))
.WillOnce(::testing::DoAll(::testing::SaveArg<0>(&capturedB), ::testing::Return(identity)));
EXPECT_CALL(model, DriftTerm(::testing::_))
.WillOnce(::testing::DoAll(::testing::SaveArg<0>(&capturedA), ::testing::Return(a)));

controller.ComputeInput(xQuery, zero, zero, zero, zero);

EXPECT_FLOAT_EQ(capturedB.at(0, 0), xQuery.at(0, 0));
EXPECT_FLOAT_EQ(capturedB.at(1, 0), xQuery.at(1, 0));
EXPECT_FLOAT_EQ(capturedA.at(0, 0), xQuery.at(0, 0));
EXPECT_FLOAT_EQ(capturedA.at(1, 0), xQuery.at(1, 0));
}

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