Robust data-driven learning and control of nonlinear systems. A Sontag's formula approach

TL;DR

This paper introduces a robust, data-driven method for learning and controlling nonlinear systems using a mixture of Gaussians and Sontag's formula, ensuring stability and robustness even with noisy data.

Contribution

It combines Sontag's formula with a mixture of Gaussians and a constrained optimization framework for unsupervised learning and control of nonlinear systems, enhancing robustness.

Findings

Successfully applied to handwriting trajectory dataset

Outperforms previous methods under noisy conditions

Guarantees Lyapunov stability and robustness

Abstract

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 modelled as a mixture of Gaussians and the 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. The proposed method can be used to program nonlinear trajectories in robotic systems through human demonstrations.