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 studies uniform stabilization and social optimality for linearquadratic (LQ) mean field control problems with multiplicative noise, whereagents are coupled via dynamics and individual costs. The state and controlweights in cost functionals are not limited to be positive semi-definite. Thisleads to an indefinite LQ mean field control problem, which may still bewell-posed due to deep nature of multiplicative noise. We first obtain a set offorward-backward stochastic differential equations (FBSDEs) from variationalanalysis, and construct a feedback control by decoupling the FBSDEs. By usingsolutions to two Riccati equations, we design a set of decentralized controllaws, which is further shown to be asymptotically social optimal. Someequivalent conditions are given for uniform stabilization of the systems withthe help of linear matrix inequalities. A numerical example is given toillustrate the effectiveness of the proposed control laws.

Indefinite Linear Quadratic Mean Field Social Control Problems with Multiplicative Noise