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

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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.
Dortmund ; Bayreuth , 2023
DOI: https://doi.org/10.48550/arXiv.2311.17596

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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 L^2 probability space, to tackle the non-Gaussian case. We present the optimal solutions for finite and infinite horizons. Moreover, we quantify the truncation error and we analyze the infinite-horizon asymptotics. We show that the limit of the optimal trajectory is the unique solution to a stationary optimization problem in the sense of probability measures. A numerical example illustrates our findings.