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arXiv · 2311.17596

A Polynomial Chaos Approach to Stochastic LQ Optimal Control: Error Bounds and Infinite-Horizon Results

Ruchuan Ou·Jonas Schießl·Michael Heinrich Baumann·Lars Grüne·Timm Faulwasser
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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 $\mathcal{L}^2$ 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.

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Ruchuan Ou, Jonas Schießl, Michael Heinrich Baumann, Lars Grüne, Timm Faulwasser. 2023-11-29. A Polynomial Chaos Approach to Stochastic LQ Optimal Control: Error Bounds and Infinite-Horizon Results. https://doi.org/10.1016/j.automatica.2025.112117.

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