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

We consider the problem of controlling the spatiotemporal probabilitydistribution of a robotic swarm that evolves according to a reflected diffusionprocess, using the space- and time-dependent drift vector field parameter asthe control variable. In contrast to previous work on control of theFokker-Planck equation, a zero-flux boundary condition is imposed on thepartial differential equation that governs the swarm probability distribution,and only bounded vector fields are considered to be admissible as controlparameters. Under these constraints, we show that any initial probabilitydistribution can be transported to a target probability distribution undercertain assumptions on the regularity of the target distribution. Inparticular, we show that if the target distribution is (essentially) bounded,has bounded first-order and second-order partial derivatives, and is boundedfrom below by a strictly positive constant, then this distribution can bereached exactly using a drift vector field that is bounded in space and time.Our proof is constructive and based on classical linear semigroup theoreticconcepts.

Controllability to Equilibria of the 1-D Fokker-Planck Equation with Zero-Flux Boundary Condition