├── .gitignore ├── LICENSE ├── README.md ├── assets ├── pendulum_output_feedback.png ├── pendulum_path_tracking.png ├── quadrotor2d_output.png └── quadrotor_state.png ├── baselines └── nlc_discrete │ ├── cartpole.py │ ├── cartpole.yaml │ ├── cartpole_with_rho.yaml │ ├── models │ ├── cartpole.pth │ ├── cartpole_lyapunov.pth │ ├── path_tracking.pth │ ├── path_tracking_lyapunov.pth │ ├── pendulum.pth │ ├── pendulum_lyapunov.pth │ └── pvtol.pth │ ├── path_tracking.py │ ├── path_tracking.yaml │ ├── path_tracking_with_rho.yaml │ ├── pendulum.py │ ├── pendulum.yaml │ ├── pendulum_with_rho.yaml │ ├── plot.py │ ├── pvtol.py │ ├── pvtol.yaml │ ├── specs │ ├── cartpole.csv │ ├── cartpole.vnnlib │ ├── cartpole_with_rho.csv │ ├── cartpole_with_rho.vnnlib │ ├── path_tracking.csv │ ├── path_tracking.vnnlib │ ├── path_tracking_with_rho.csv │ ├── path_tracking_with_rho.vnnlib │ ├── pendulum.csv │ ├── pendulum.vnnlib │ ├── pendulum_with_rho.csv │ ├── pendulum_with_rho.vnnlib │ ├── pvtol_0.vnnlib │ ├── pvtol_1.vnnlib │ ├── pvtol_10.vnnlib │ ├── pvtol_11.vnnlib │ ├── pvtol_12.vnnlib │ ├── pvtol_13.vnnlib │ ├── pvtol_14.vnnlib │ ├── pvtol_15.vnnlib │ ├── pvtol_16.vnnlib │ ├── pvtol_17.vnnlib │ ├── pvtol_18.vnnlib │ ├── pvtol_19.vnnlib │ ├── pvtol_2.vnnlib │ ├── pvtol_20.vnnlib │ ├── pvtol_21.vnnlib │ ├── pvtol_22.vnnlib │ ├── pvtol_23.vnnlib │ ├── pvtol_24.vnnlib │ ├── pvtol_25.vnnlib │ ├── pvtol_26.vnnlib │ ├── pvtol_27.vnnlib │ ├── pvtol_28.vnnlib │ ├── pvtol_29.vnnlib │ ├── pvtol_3.vnnlib │ ├── pvtol_30.vnnlib │ ├── pvtol_31.vnnlib │ ├── pvtol_32.vnnlib │ ├── pvtol_33.vnnlib │ ├── pvtol_34.vnnlib │ ├── pvtol_35.vnnlib │ ├── pvtol_36.vnnlib │ ├── pvtol_37.vnnlib │ ├── pvtol_38.vnnlib │ ├── pvtol_39.vnnlib │ ├── pvtol_4.vnnlib │ ├── pvtol_40.vnnlib │ ├── pvtol_41.vnnlib │ ├── pvtol_42.vnnlib │ ├── pvtol_43.vnnlib │ ├── pvtol_44.vnnlib │ ├── pvtol_45.vnnlib │ ├── pvtol_46.vnnlib │ ├── pvtol_47.vnnlib │ ├── pvtol_48.vnnlib │ ├── pvtol_49.vnnlib │ ├── pvtol_5.vnnlib │ ├── pvtol_50.vnnlib │ ├── pvtol_51.vnnlib │ ├── pvtol_52.vnnlib │ ├── pvtol_53.vnnlib │ ├── pvtol_54.vnnlib │ ├── pvtol_55.vnnlib │ ├── pvtol_56.vnnlib │ ├── pvtol_57.vnnlib │ ├── pvtol_58.vnnlib │ ├── pvtol_59.vnnlib │ ├── pvtol_6.vnnlib │ ├── pvtol_60.vnnlib │ ├── pvtol_61.vnnlib │ ├── pvtol_62.vnnlib │ ├── pvtol_63.vnnlib │ ├── pvtol_7.vnnlib │ ├── pvtol_8.vnnlib │ ├── pvtol_9.vnnlib │ └── pvtol_instances.csv │ └── split_lyapunov.py ├── examples ├── __init__.py ├── config │ ├── path_tracking_state_training.yaml │ ├── pendulum_output_training.yaml │ ├── pendulum_state_training.yaml │ ├── pendulum_state_training_reproduce.yaml │ ├── pendulum_state_training_small_torque.yaml │ ├── quadrotor2d_output_training.yaml │ ├── quadrotor2d_state_training.yaml │ ├── train_template.yaml │ └── user │ │ ├── path_tracking_state_training_default.yaml │ │ ├── pendulum_output_training_default.yaml │ │ ├── pendulum_state_training_default.yaml │ │ ├── quadrotor2d_default_user.yaml │ │ ├── quadrotor2d_output_training_default.yaml │ │ └── quadrotor2d_state_training_default.yaml ├── data │ ├── cartpole │ │ ├── controller_lqr_[8, 8, 8].pth │ │ └── controller_lqr_[8, 8].pth │ ├── pendulum │ │ ├── output_feedback │ │ │ ├── controller_[8, 8, 8].pth │ │ │ ├── lyapunov_init.pth │ │ │ ├── observer_[8, 8].pth │ │ │ └── sos_controller.pkl │ │ └── state_feedback │ │ │ ├── controller_init.pth │ │ │ ├── lyaloss_init.pth │ │ │ └── lyaloss_lqr.pth │ └── quadrotor2d │ │ ├── Vmin_x_pgd_init.pth │ │ ├── controller_lqr_[8, 8].pth │ │ ├── lyaloss_init.pth │ │ ├── output_feedback │ │ ├── controller_[8, 8].pth │ │ └── observer_[8, 8].pth │ │ └── x_pgd_verifier_init.pth ├── path_tracking_state_training.py ├── pendulum_output_training.py ├── pendulum_state_training.py ├── pvtol_training.py ├── quadrotor2d_output_training.py └── quadrotor2d_state_training.py ├── models ├── path_tracking_state_feedback.pth ├── path_tracking_state_feedback_quadratic.pth ├── path_tracking_state_feedback_small_torque.pth ├── pendulum_output_feedback.pth ├── pendulum_output_feedback_nn.pth ├── pendulum_output_feedback_small_torque.pth ├── pendulum_state_feedback.pth ├── pendulum_state_feedback_quadratic.pth ├── pendulum_state_feedback_small_torque.pth ├── pvtol_state_feedback.pth ├── quadrotor2d_output_feedback.pth └── quadrotor2d_state_feedback.pth ├── neural_lyapunov_training ├── __init__.py ├── arguments.py ├── bisect.py ├── controllers.py ├── dynamical_system.py ├── generate_vnnlib.py ├── levelset.py ├── lyapunov.py ├── models.py ├── neural_lyapunov_arguments.py ├── optimize_graph.py ├── output_train_utils.py ├── path_tracking.py ├── pendulum.py ├── pvtol.py ├── quadrotor2d.py ├── split_lyapunov_loss.py ├── train_utils.py └── try_verifier.py ├── requirements.txt ├── setup.py ├── tests ├── test_controllers.py ├── test_lyapunov.py ├── test_pendulum.py └── test_quadrotor2d.py └── verification ├── complete_verifier ├── path_tracking_state_feedback_lyapunov_in_levelset.yaml ├── path_tracking_state_feedback_lyapunov_small_torque_in_levelset.yaml ├── path_tracking_state_feedback_quadratic_lyapunov_in_levelset.yaml ├── pendulum_output_feedback_lyapunov_in_levelset.yaml ├── pendulum_output_feedback_lyapunov_nn_in_levelset.yaml ├── pendulum_output_feedback_lyapunov_small_torque_in_levelset.yaml ├── pendulum_state_feedback_lyapunov_in_levelset.yaml ├── pendulum_state_feedback_lyapunov_small_torque_in_levelset.yaml ├── pendulum_state_feedback_quadratic_lyapunov_in_levelset.yaml ├── pvtol_state_feedback_lyapunov_in_levelset.yaml ├── quadrotor2d_output_feedback_lyapunov_in_levelset.yaml ├── quadrotor2d_state_feedback_lyapunov_in_levelset.yaml └── specs ├── path_tracking_state_feedback.csv ├── path_tracking_state_feedback_0.vnnlib ├── path_tracking_state_feedback_1.vnnlib ├── path_tracking_state_feedback_2.vnnlib ├── path_tracking_state_feedback_3.vnnlib ├── path_tracking_state_feedback_quadratic.csv ├── path_tracking_state_feedback_quadratic_0.vnnlib ├── path_tracking_state_feedback_quadratic_1.vnnlib ├── path_tracking_state_feedback_quadratic_2.vnnlib ├── path_tracking_state_feedback_quadratic_3.vnnlib ├── path_tracking_state_feedback_small_torque.csv ├── path_tracking_state_feedback_small_torque_0.vnnlib ├── path_tracking_state_feedback_small_torque_1.vnnlib ├── path_tracking_state_feedback_small_torque_2.vnnlib ├── path_tracking_state_feedback_small_torque_3.vnnlib ├── pendulum_output_feedback.csv ├── pendulum_output_feedback_0.vnnlib ├── pendulum_output_feedback_1.vnnlib ├── pendulum_output_feedback_2.vnnlib ├── pendulum_output_feedback_3.vnnlib ├── pendulum_output_feedback_4.vnnlib ├── pendulum_output_feedback_5.vnnlib ├── pendulum_output_feedback_6.vnnlib ├── pendulum_output_feedback_7.vnnlib ├── pendulum_output_feedback_nn.csv ├── pendulum_output_feedback_nn_0.vnnlib ├── pendulum_output_feedback_nn_1.vnnlib ├── pendulum_output_feedback_nn_2.vnnlib ├── pendulum_output_feedback_nn_3.vnnlib ├── pendulum_output_feedback_nn_4.vnnlib ├── pendulum_output_feedback_nn_5.vnnlib ├── pendulum_output_feedback_nn_6.vnnlib ├── pendulum_output_feedback_nn_7.vnnlib ├── pendulum_output_feedback_small_torque.csv ├── pendulum_output_feedback_small_torque_0.vnnlib ├── pendulum_output_feedback_small_torque_1.vnnlib ├── pendulum_output_feedback_small_torque_2.vnnlib ├── pendulum_output_feedback_small_torque_3.vnnlib ├── pendulum_output_feedback_small_torque_4.vnnlib ├── pendulum_output_feedback_small_torque_5.vnnlib ├── pendulum_output_feedback_small_torque_6.vnnlib ├── pendulum_output_feedback_small_torque_7.vnnlib ├── pendulum_state_feedback.csv ├── pendulum_state_feedback_0.vnnlib ├── pendulum_state_feedback_1.vnnlib ├── pendulum_state_feedback_2.vnnlib ├── pendulum_state_feedback_3.vnnlib ├── pendulum_state_feedback_quadratic.csv ├── pendulum_state_feedback_quadratic_0.vnnlib ├── pendulum_state_feedback_quadratic_1.vnnlib ├── pendulum_state_feedback_quadratic_2.vnnlib ├── pendulum_state_feedback_quadratic_3.vnnlib ├── pendulum_state_feedback_quadratic_450.csv ├── pendulum_state_feedback_quadratic_450_0.vnnlib ├── pendulum_state_feedback_quadratic_450_1.vnnlib ├── pendulum_state_feedback_quadratic_450_2.vnnlib ├── pendulum_state_feedback_quadratic_450_3.vnnlib ├── pendulum_state_feedback_small_torque.csv ├── pendulum_state_feedback_small_torque_0.vnnlib ├── pendulum_state_feedback_small_torque_1.vnnlib ├── pendulum_state_feedback_small_torque_2.vnnlib ├── pendulum_state_feedback_small_torque_3.vnnlib ├── pvtol_state_feedback.csv ├── pvtol_state_feedback_0.vnnlib ├── pvtol_state_feedback_1.vnnlib ├── pvtol_state_feedback_10.vnnlib ├── pvtol_state_feedback_11.vnnlib ├── pvtol_state_feedback_2.vnnlib ├── pvtol_state_feedback_3.vnnlib ├── pvtol_state_feedback_4.vnnlib ├── pvtol_state_feedback_5.vnnlib ├── pvtol_state_feedback_6.vnnlib ├── pvtol_state_feedback_7.vnnlib ├── pvtol_state_feedback_8.vnnlib ├── pvtol_state_feedback_9.vnnlib ├── quadrotor2d_output_feedback.csv ├── quadrotor2d_output_feedback_0.vnnlib ├── quadrotor2d_output_feedback_1.vnnlib ├── quadrotor2d_output_feedback_10.vnnlib ├── quadrotor2d_output_feedback_11.vnnlib ├── quadrotor2d_output_feedback_12.vnnlib ├── quadrotor2d_output_feedback_13.vnnlib ├── quadrotor2d_output_feedback_14.vnnlib ├── quadrotor2d_output_feedback_15.vnnlib ├── quadrotor2d_output_feedback_2.vnnlib ├── quadrotor2d_output_feedback_3.vnnlib ├── quadrotor2d_output_feedback_4.vnnlib ├── quadrotor2d_output_feedback_5.vnnlib ├── quadrotor2d_output_feedback_6.vnnlib ├── quadrotor2d_output_feedback_7.vnnlib ├── quadrotor2d_output_feedback_8.vnnlib ├── quadrotor2d_output_feedback_9.vnnlib ├── quadrotor2d_output_feedback_x_next.csv ├── quadrotor2d_output_feedback_x_next_0.vnnlib ├── quadrotor2d_output_feedback_x_next_1.vnnlib ├── quadrotor2d_output_feedback_x_next_10.vnnlib ├── quadrotor2d_output_feedback_x_next_11.vnnlib ├── quadrotor2d_output_feedback_x_next_12.vnnlib ├── quadrotor2d_output_feedback_x_next_13.vnnlib ├── quadrotor2d_output_feedback_x_next_14.vnnlib ├── quadrotor2d_output_feedback_x_next_15.vnnlib ├── quadrotor2d_output_feedback_x_next_2.vnnlib ├── quadrotor2d_output_feedback_x_next_3.vnnlib ├── quadrotor2d_output_feedback_x_next_4.vnnlib ├── quadrotor2d_output_feedback_x_next_5.vnnlib ├── quadrotor2d_output_feedback_x_next_6.vnnlib ├── quadrotor2d_output_feedback_x_next_7.vnnlib ├── quadrotor2d_output_feedback_x_next_8.vnnlib ├── quadrotor2d_output_feedback_x_next_9.vnnlib ├── quadrotor2d_state_feedback.csv ├── quadrotor2d_state_feedback_0.vnnlib ├── quadrotor2d_state_feedback_1.vnnlib ├── quadrotor2d_state_feedback_10.vnnlib ├── quadrotor2d_state_feedback_11.vnnlib ├── quadrotor2d_state_feedback_2.vnnlib ├── quadrotor2d_state_feedback_3.vnnlib ├── quadrotor2d_state_feedback_4.vnnlib ├── quadrotor2d_state_feedback_5.vnnlib ├── quadrotor2d_state_feedback_6.vnnlib ├── 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