Thank you for your interesting work. We have conducted a follow-up study on your research, where we solved for a controller and certified the Lyapunov conditions for arbitrary nonlinear dynamical systems in the discrete-time setting: https://github.com/jlwu002/nlc_discrete (NeurIPS 2023), paper.
We noticed that the controller used in the paper (and code) for Path Following dynamics does not have a bias term, meaning that the controller $u = 0$ at the equilibrium point $(d_e, \theta_e) = 0$. This does not seem feasible for the path-following setting: when the distance error and angle error are both zero (at equilibrium point), we still need the steering angle to ensure the object is following the unit circle target trajectory.
Thank you for your interesting work. We have conducted a follow-up study on your research, where we solved for a controller and certified the Lyapunov conditions for arbitrary nonlinear dynamical systems in the discrete-time setting: https://github.com/jlwu002/nlc_discrete (NeurIPS 2023), paper.
We noticed that the controller used in the paper (and code) for Path Following dynamics does not have a bias term, meaning that the controller $u = 0$ at the equilibrium point $(d_e, \theta_e) = 0$. This does not seem feasible for the path-following setting: when the distance error and angle error are both zero (at equilibrium point), we still need the steering angle to ensure the object is following the unit circle target trajectory.