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

In this paper, our goal is to study fundamental foundations of linearquadratic Gaussian (LQG) control problems for stochastic linear time-invariantsystems via Lagrangian duality of semidefinite programming (SDP) problems. Inparticular, we derive an SDP formulation of the finite-horizon LQG problem, andits Lagrangian duality. Moreover, we prove that Riccati equation for LQG can bederived the KKT optimality condition of the corresponding SDP problem. Besides,the proposed primal problem efficiently decouples the system matrices and thegain matrix. This allows us to develop new convex relaxations of non-convexstructured control design problems such as the decentralized control problem.We expect that this work would provide new insights on the LQG problem and maypotentially facilitate developments of new formulations of various optimalcontrol problems. Numerical examples are given to demonstrate the effectivenessof the proposed methods.

On the Semidefinite Duality of Finite-Horizon LQG Problem