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 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.

Subjects

Linear–quadratic regulator | Non-Gaussian distributions | Polynomial chaos | Stochastic optimal control | Stochastic stationarity

DDC Class

519: Applied Mathematics, Probabilities

Funding(s)

Projekt DEAL

Publication version

publishedVersion

Lizenz

https://creativecommons.org/licenses/by/4.0/

Name

1-s2.0-S0005109825000081-main.pdf

Type

Main Article

Size

1.08 MB

Format

Adobe PDF

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