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 is the first of a two part paper investigating the geometry of theintegrator reach sets, and the applications thereof. In this Part I, assumingbox-valued input uncertainties, we establish that this compact convex reach setis semialgebraic, translated zonoid, and not a spectrahedron. We derive theparametric as well as the implicit representation of the boundary of this reachset. We also deduce the closed form formula for the volume and diameter of thisset, and discuss their scaling with state dimension and time. We point out thatthese results may be utilized in benchmarking the performance of the reach setover-approximation algorithms.

The Curious Case of Integrator Reach Sets, Part I: Basic Theory