Data-driven Stochastic Output-Feedback Predictive Control: Recursive Feasibility through Interpolated Initial Conditions

Guanru Pan, Ruchuan Ou, Timm Faulwasser
Proceedings of The 5th Annual Learning for Dynamics and Control Conference, PMLR 211:980-992, 2023.

Abstract

This paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control Problem (OCP), which allows for forward prediction and optimization of statistical distributions of inputs and outputs. Our approach avoids the use of parametric system models. Instead it is based on previously recorded data and on a recently proposed stochastic variant of Willems’ fundamental lemma. The stochastic variant of the lemma is applicable to linear dynamics subject to a large class of stochastic disturbances of Gaussian or non-Gaussian nature. To ensure recursive feasibility, the initial condition of the OCP—which consists of information about past inputs and outputs—is considered as an extra decision variable of the OCP. We provide sufficient conditions for recursive feasibility of the proposed scheme as well as a bound on the asymptotic average performance. Finally, a numerical example illustrates the efficacy and the closed-loop properties of the proposed scheme.

Cite this Paper

BibTeX
@InProceedings{pmlr-v211-pan23a, title = {Data-driven Stochastic Output-Feedback Predictive Control: Recursive Feasibility through Interpolated Initial Conditions}, author = {Pan, Guanru and Ou, Ruchuan and Faulwasser, Timm}, booktitle = {Proceedings of The 5th Annual Learning for Dynamics and Control Conference}, pages = {980--992}, year = {2023}, editor = {Matni, Nikolai and Morari, Manfred and Pappas, George J.}, volume = {211}, series = {Proceedings of Machine Learning Research}, month = {15--16 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v211/pan23a/pan23a.pdf}, url = {https://proceedings.mlr.press/v211/pan23a.html}, abstract = {This paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control Problem (OCP), which allows for forward prediction and optimization of statistical distributions of inputs and outputs. Our approach avoids the use of parametric system models. Instead it is based on previously recorded data and on a recently proposed stochastic variant of Willems’ fundamental lemma. The stochastic variant of the lemma is applicable to linear dynamics subject to a large class of stochastic disturbances of Gaussian or non-Gaussian nature. To ensure recursive feasibility, the initial condition of the OCP—which consists of information about past inputs and outputs—is considered as an extra decision variable of the OCP. We provide sufficient conditions for recursive feasibility of the proposed scheme as well as a bound on the asymptotic average performance. Finally, a numerical example illustrates the efficacy and the closed-loop properties of the proposed scheme. } }
Endnote
%0 Conference Paper %T Data-driven Stochastic Output-Feedback Predictive Control: Recursive Feasibility through Interpolated Initial Conditions %A Guanru Pan %A Ruchuan Ou %A Timm Faulwasser %B Proceedings of The 5th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2023 %E Nikolai Matni %E Manfred Morari %E George J. Pappas %F pmlr-v211-pan23a %I PMLR %P 980--992 %U https://proceedings.mlr.press/v211/pan23a.html %V 211 %X This paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control Problem (OCP), which allows for forward prediction and optimization of statistical distributions of inputs and outputs. Our approach avoids the use of parametric system models. Instead it is based on previously recorded data and on a recently proposed stochastic variant of Willems’ fundamental lemma. The stochastic variant of the lemma is applicable to linear dynamics subject to a large class of stochastic disturbances of Gaussian or non-Gaussian nature. To ensure recursive feasibility, the initial condition of the OCP—which consists of information about past inputs and outputs—is considered as an extra decision variable of the OCP. We provide sufficient conditions for recursive feasibility of the proposed scheme as well as a bound on the asymptotic average performance. Finally, a numerical example illustrates the efficacy and the closed-loop properties of the proposed scheme.
APA
Pan, G., Ou, R. & Faulwasser, T.. (2023). Data-driven Stochastic Output-Feedback Predictive Control: Recursive Feasibility through Interpolated Initial Conditions. Proceedings of The 5th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 211:980-992 Available from https://proceedings.mlr.press/v211/pan23a.html.

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