Ou, RuchuanRuchuanOuSchießl, JonasJonasSchießlBaumann, Michael HeinrichMichael HeinrichBaumannGrüne, LarsLarsGrüneFaulwasser, TimmTimmFaulwasser2025-02-142025-02-142025-02-06Automatica 174: 112117 (2025)https://hdl.handle.net/11420/54225The 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.en0005-10982025Elsevierhttps://creativecommons.org/licenses/by/4.0/Linear–quadratic regulator | Non-Gaussian distributions | Polynomial chaos | Stochastic optimal control | Stochastic stationarityNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesJournal Articlehttps://doi.org/10.15480/882.1460210.1016/j.automatica.2025.11211710.15480/882.14602Journal Article