A polynomial chaos approach to stochastic LQ optimal control: Error bounds and infinite-horizon results

The stochastic linear–quadratic regulator problem subject to Gaussian disturbances is well known and usually addressed via a moment-based reformulation. Here, we leverage polynomial chaos expansions, which model random variables via series expansions in a suitable L2 probability space, to tackle the...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 174; p. 112117
Main Authors Ou, Ruchuan, Schießl, Jonas, Baumann, Michael Heinrich, Grüne, Lars, Faulwasser, Timm
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2025
Subjects
Linear–quadratic regulator
Non-Gaussian distributions
Polynomial chaos
Stochastic optimal control
Stochastic stationarity
Polynomial chaos
Stochastic stationarity
Stochastic optimal control
Non-Gaussian distributions
Linear–quadratic regulator
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ISSN0005-1098
DOI10.1016/j.automatica.2025.112117

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Summary:The stochastic linear–quadratic regulator problem subject to Gaussian disturbances is well known and usually addressed via a moment-based reformulation. Here, we leverage polynomial chaos expansions, which model random variables via series expansions in a suitable L2 probability space, to tackle the non-Gaussian case. We present the optimal solutions for finite and infinite horizons and we analyze the infinite-horizon asymptotics. We show that the limit of the optimal state-input trajectory is the unique solution to a corresponding stochastic stationary optimization problem in the sense of probability measures. Moreover, we provide a constructive error analysis for finite-dimensional polynomial chaos approximations of the optimal solutions and of the optimal stationary pair in non-Gaussian settings. A numerical example illustrates our findings.
ISSN:0005-1098
DOI:10.1016/j.automatica.2025.112117