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Mathematics > Optimization and Control

arXiv:2108.06687 (math)
[Submitted on 15 Aug 2021]

Title:On the Semidefinite Duality of Finite-Horizon LQG Problem

Authors:Donghwan Lee
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Abstract:In this paper, our goal is to study fundamental foundations of linear quadratic Gaussian (LQG) control problems for stochastic linear time-invariant systems via Lagrangian duality of semidefinite programming (SDP) problems. In particular, we derive an SDP formulation of the finite-horizon LQG problem, and its Lagrangian duality. Moreover, we prove that Riccati equation for LQG can be derived the KKT optimality condition of the corresponding SDP problem. Besides, the proposed primal problem efficiently decouples the system matrices and the gain matrix. This allows us to develop new convex relaxations of non-convex structured control design problems such as the decentralized control problem. We expect that this work would provide new insights on the LQG problem and may potentially facilitate developments of new formulations of various optimal control problems. Numerical examples are given to demonstrate the effectiveness of the proposed methods.
Comments: arXiv admin note: substantial text overlap with arXiv:2108.01457
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
Cite as: arXiv:2108.06687 [math.OC]
  (or arXiv:2108.06687v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.06687

Submission history

From: Donghwan Lee [view email]
[v1] Sun, 15 Aug 2021 08:12:17 UTC (25 KB)
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