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

Department of Data Science

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

4 Citations (Scopus)

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. © 2022 IEEE.

Original language	English
Title of host publication	2022 IEEE 61st Conference on Decision and Control (CDC)
Publisher	IEEE
Pages	1039-1044
ISBN (Electronic)	9781665467612, 978-1-6654-6760-5
ISBN (Print)	978-1-6654-6762-9
DOIs	https://doi.org/10.1109/CDC51059.2022.9992921
Publication status	Published - Dec 2022
Event	61st IEEE Conference on Decision and Control (CDC 2022) - Cancún, Mexico Duration: 6 Dec 2022 → 9 Dec 2022

Publication series

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

Conference

Conference	61st IEEE Conference on Decision and Control (CDC 2022)
Abbreviated title	CDC22
Place	Mexico
City	Cancún
Period	6/12/22 → 9/12/22

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10.1109/CDC51059.2022.9992921

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title = "Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems",

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. {\textcopyright} 2022 IEEE.",

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

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doi = "10.1109/CDC51059.2022.9992921",

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isbn = "978-1-6654-6762-9",

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note = "61st IEEE Conference on Decision and Control (CDC 2022), CDC22 ; Conference date: 06-12-2022 Through 09-12-2022",

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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). Proceedings of the IEEE Conference on Decision and Control, IEEE, pp. 1039-1044, 61st IEEE Conference on Decision and Control (CDC 2022), Cancún, 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). IEEE, 2022. p. 1039-1044 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Operator-valued Kernels and Control of Infinite dimensional Dynamic Systems

AU - Aubin-Frankowski, Pierre-Cyril

AU - Bensoussan, Alain

PY - 2022/12

Y1 - 2022/12

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. © 2022 IEEE.

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. © 2022 IEEE.

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U2 - 10.1109/CDC51059.2022.9992921

DO - 10.1109/CDC51059.2022.9992921

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 978-1-6654-6762-9

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 1039

EP - 1044

BT - 2022 IEEE 61st Conference on Decision and Control (CDC)

PB - IEEE

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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