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

Safety is a critical property for control systems in medicine,transportation, manufacturing, and other applications, and can be defined asensuring positive invariance of a predefined safe set. One approach to ensuringsafety is to construct a Control Barrier Function (CBF) such that the system issafe when the CBF is nonnegative, and then choose a control input to ensurenonnegativity of the CBF at each time step, provided that such an input exists.This paper investigates the problems of verification and synthesis of controlbarrier functions. In the area of verification, we use the algebraic-geometricPositivstellensatz to construct convex equivalent conditions for a CBF toensure safety. We extend these conditions to control policies based on unionsand intersections of CBFs, high-order CBFs, and systems with trigonometricdynamics, actuation constraints, and Euler-Lagrange dynamics. In the area ofsynthesis, we propose algorithms for constructing CBFs, namely, analternating-descent approach, a local CBF approach, and a Newton's methodapproach. We prove that the latter algorithm guarantees local convergence to aCBF at a quadratic rate.

A Semi-Algebraic Framework for Verification and Synthesis of Control Barrier Functions