Discounted cost linear quadratic Gaussian control for descriptor systems

We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterise the feasibility of this problem using a linear matrix inequality. In particular,...

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Bibliographic Details
Published inInternational journal of control Vol. 95; no. 5; pp. 1349 - 1362
Main Authors Mena, Hermann, Pfurtscheller, Lena-Maria, Voigt, Matthias
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.05.2022
Taylor & Francis Ltd
Subjects
Descriptor systems
dissipation inequality
Fluid dynamics
Kalman-Yakubovich-Popov inequality
Linear matrix inequalities
Linear quadratic Gaussian control
Mathematical analysis
Navier-Stokes equation
Optimal control
Riccati equation
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Summary:We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterise the feasibility of this problem using a linear matrix inequality. In particular, conditions for existence and uniqueness of optimal controls are derived, which are weaker compared to the standard approaches in the literature. We further show that also for the stochastic problem, the optimal control is given in terms of the stabilising solution of the Lur'e equation, which generalises the algebraic Riccati equation. We conclude our paper by examining an application of our theory to fluid dynamics problems.
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2020.1854865