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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this article we study the optimal control problem with quadraticfunctionals for a linear Volterra integro-differential equation in Hilbertspaces. With the finite history seen as an (additional) initial datum for theevolution, following the variational approach utilized in the study of thelinear-quadratic problem for memoryless infinite dimensional systems, we attaina closed-loop form of the unique optimal control via certain operators that areshown to solve a coupled system of quadratic differential equations. Thisresult provides a first extension to the partial differential equations realmof the Riccati-based theory recently devised by L. Pandolfi in a finitedimensional context.

Riccati-based solution to the optimal control of linear evolution equations with finite memory