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

Title data

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

Official URL: Volltext

Project information

Project title:
Project's official title
Project's id
Stochastic Optimal Control and MPC - Dissipativity, Risk, and Performance
499435839

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type: Preprint, postprint
Refereed: Yes
Keywords: Linear-quadratic regulator; stochastic optimal control; polynomial chaos; stochastic stationarity; non-Gaussian distributions
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions
Research Institutions > Central research institutes
Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 01 Dec 2023 05:59
Last Modified: 01 Dec 2023 05:59
URI: https://eref.uni-bayreuth.de/id/eprint/87955