Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems

Pierre Cyril Aubin-Frankowski; Alain Bensoussan

doi:10.1109/CDC51059.2022.9992921

Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems

Pierre Cyril Aubin-Frankowski
, Alain Bensoussan

University of Texas

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in [1] for finite dimensional systems. We show that this result extends to infinite dimensional systems, i.e. control of linear partial differential equations. The quadratic objective paired with the linear dynamics encode the relevant kernel, defining a Hilbert space of controlled trajectories, for which we obtain a concise formula based on the solution of the differential Riccati equation. This paves the way to applying representer theorems from kernel methods to solve infinite dimensional optimal control problems.

Original language	English
Title of host publication	2022 IEEE 61st Conference on Decision and Control, CDC 2022
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1039-1044
Number of pages	6
ISBN (Electronic)	9781665467612
DOIs	https://doi.org/10.1109/CDC51059.2022.9992921
Publication status	Published - 1 Jan 2022
Event	61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico Duration: 6 Dec 2022 → 9 Dec 2022

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2022-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	61st IEEE Conference on Decision and Control, CDC 2022
Country/Territory	Mexico
City	Cancun
Period	6/12/22 → 9/12/22

Access to Document

10.1109/CDC51059.2022.9992921

Cite this

Aubin-Frankowski, P. C., & Bensoussan, A. (2022). Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems. In 2022 IEEE 61st Conference on Decision and Control, CDC 2022 (pp. 1039-1044). (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC51059.2022.9992921

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abstract = "The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in [1] for finite dimensional systems. We show that this result extends to infinite dimensional systems, i.e. control of linear partial differential equations. The quadratic objective paired with the linear dynamics encode the relevant kernel, defining a Hilbert space of controlled trajectories, for which we obtain a concise formula based on the solution of the differential Riccati equation. This paves the way to applying representer theorems from kernel methods to solve infinite dimensional optimal control problems.",

author = "Aubin-Frankowski, \{Pierre Cyril\} and Alain Bensoussan",

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Aubin-Frankowski, PC & Bensoussan, A 2022, Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems. in 2022 IEEE 61st Conference on Decision and Control, CDC 2022. Proceedings of the IEEE Conference on Decision and Control, vol. 2022-December, Institute of Electrical and Electronics Engineers Inc., pp. 1039-1044, 61st IEEE Conference on Decision and Control, CDC 2022, Cancun, Mexico, 6/12/22. https://doi.org/10.1109/CDC51059.2022.9992921

Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems. / Aubin-Frankowski, Pierre Cyril; Bensoussan, Alain.
2022 IEEE 61st Conference on Decision and Control, CDC 2022. Institute of Electrical and Electronics Engineers Inc., 2022. p. 1039-1044 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in [1] for finite dimensional systems. We show that this result extends to infinite dimensional systems, i.e. control of linear partial differential equations. The quadratic objective paired with the linear dynamics encode the relevant kernel, defining a Hilbert space of controlled trajectories, for which we obtain a concise formula based on the solution of the differential Riccati equation. This paves the way to applying representer theorems from kernel methods to solve infinite dimensional optimal control problems.

AB - The Linear Quadratic Regulator (LQR), which is arguably the most classical problem in control theory, was recently related to kernel methods in [1] for finite dimensional systems. We show that this result extends to infinite dimensional systems, i.e. control of linear partial differential equations. The quadratic objective paired with the linear dynamics encode the relevant kernel, defining a Hilbert space of controlled trajectories, for which we obtain a concise formula based on the solution of the differential Riccati equation. This paves the way to applying representer theorems from kernel methods to solve infinite dimensional optimal control problems.

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T2 - 61st IEEE Conference on Decision and Control, CDC 2022

Y2 - 6 December 2022 through 9 December 2022

ER -

Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems

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