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

Titelangaben

Ou, Ruchuan ; Schießl, Jonas ; Baumann, Michael Heinrich ; Grüne, Lars ; Faulwasser, Timm:
A polynomial chaos approach to stochastic LQ optimal control : Error bounds and infinite-horizon results.
In: Automatica. Bd. 174 (2025) . - 112117.
ISSN 1873-2836
DOI: https://doi.org/10.1016/j.automatica.2025.112117

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Abstract

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.