Erratum to “Learning to Boost the Performance of Stable Nonlinear Systems”

Abstract

This addresses errors in [1]. Due to a production error, Figs. 4, 5, 6, 8, and 9 are not rendering correctly in the article PDF. The correct figures are as follows. Figure 4. Mountains—Closed-loop trajectories before training (left) and after training (middle and right) over 100 randomly sampled initial conditions marked with $\circ$. Snapshots taken at time-instants τ. Colored (gray) lines show the trajectories in [0, τi] ([τi, ∞)). Colored balls (and their radius) represent the agents (and their size for collision avoidance). Figure 5. Mountains—Closed-loop trajectories after 25%, 50% and 75% of the total training whose closed-loop trajectory is shown in Fig. 4. Even if the performance can be further optimized, stability is always guaranteed. Figure 6. Mountains—Closed-loop trajectories after training. (Left and middle) Controller tested over a system with mass uncertainty (-10% and +10%, respectively). (Right) Trained controller with safety promotion through (45). Training initial conditions marked with $\circ$. Snapshots taken at time-instants τ. Colored (gray) lines show the trajectories in [0, τi] ([τi, ∞)). Colored balls (and their radius) represent the agents (and their size for collision avoidance). Figure 8. Mountains—Closed-loop trajectories when using the online policy given by (48). Snapshots of three trajectories starting at different test initial conditions. Figure 9. Mountains—Three different closed-loop trajectories after training a REN controller without ${\mathcal{L}}_{2}$ stability guarantees over 100 randomly sampled initial conditions marked with $\circ$. Colored (gray) lines show the trajectories in (after) the training time interval.