Data-driven learning and control of nonlinear system dynamics: A robust-learning approach via Sontag's control formula

This work falls into the field of discovering the dynamic equations of stabilizable nonlinear systems, via a learning-and-control algorithm to process the data sets of trajectories previously obtained. To this end, an interlaced method to learn and control nonlinear system dynamics from a set of demonstrations is proposed, under a constrained optimization framework for the unsupervised learning process. The nonlinear system is modeled as a mixture of Gaussians and Sontag's formula together with its associated Control Lyapunov Function is proposed for learning and control. Lyapunov stability and robustness in noisy data environments are guaranteed, as a result of the inclusion of control in the learning-optimization problem. The performances are validated through a well-known dataset of demonstrations with handwriting complex trajectories, succeeding in all of them and outperforming previous methods under bounded disturbances, possibly coming from inaccuracies, imperfect demonstrations, or noisy datasets. As a result, the proposed interlaced solution yields a good performance trade-off between reproductions and robustness. Therefore, this work sheds some more light on the automatic discovery of nonlinear dynamics from noisy raw data.