English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper presents a theoretical overview of a Neural Contraction Metric(NCM): a neural network model of an optimal contraction metric andcorresponding differential Lyapunov function, the existence of which is anecessary and sufficient condition for incremental exponential stability ofnon-autonomous nonlinear system trajectories. Its innovation lies in providingformal robustness guarantees for learning-based control frameworks, utilizingcontraction theory as an analytical tool to study the nonlinear stability oflearned systems via convex optimization. In particular, we rigorously show inthis paper that, by regarding modeling errors of the learning schemes asexternal disturbances, the NCM control is capable of obtaining an explicitbound on the distance between a time-varying target trajectory and perturbedsolution trajectories, which exponentially decreases with time even under thepresence of deterministic and stochastic perturbation. These useful featurespermit simultaneous synthesis of a contraction metric and associated controllaw by a neural network, thereby enabling real-time computable and probablyrobust learning-based control for general control-affine nonlinear systems.

A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability