  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.
