The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
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Récemment, la théorie du contrôle utilisant l’apprentissage automatique, utile pour le contrôle de systèmes inconnus, a attiré une attention considérable. Cette étude se concentre sur un tel sujet avec des problèmes de contrôle optimal pour des systèmes non linéaires inconnus. Étant donné que les contrôleurs optimaux sont conçus sur la base de modèles mathématiques des systèmes, il est difficile d’obtenir des modèles avec une connaissance insuffisante des systèmes. Les fonctions du noyau sont prometteuses pour développer des modèles basés sur les données avec des connaissances limitées. Cependant, les formes complexes de ces modèles basés sur le noyau rendent difficile la conception des contrôleurs optimaux. La conception correspond à la résolution des équations de Hamilton-Jacobi (HJ) car leurs solutions fournissent des contrôleurs optimaux. Par conséquent, le but de cette étude est de dériver certains modèles basés sur le noyau pour lesquels les équations HJ sont résolues dans un sens exact, ce qui constitue une version étendue des travaux antérieurs des auteurs. Les équations HJ sont décomposées en équations matricielles algébriques traitables et en fonctions non linéaires. La résolution des équations matricielles permet d'obtenir les contrôleurs optimaux du modèle. Une simulation numérique démontre que les modèles et contrôleurs basés sur le noyau sont développés avec succès.
Yuji ITO
TOYOTA CENTRAL R&D LABS., INC.
Kenji FUJIMOTO
Kyoto University
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Yuji ITO, Kenji FUJIMOTO, "Kernel-Based Hamilton-Jacobi Equations for Data-Driven Optimal Control: The General Case" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 1, pp. 1-10, January 2022, doi: 10.1587/transfun.2021EAI0002.
Abstract: Recently, control theory using machine learning, which is useful for the control of unknown systems, has attracted significant attention. This study focuses on such a topic with optimal control problems for unknown nonlinear systems. Because optimal controllers are designed based on mathematical models of the systems, it is challenging to obtain models with insufficient knowledge of the systems. Kernel functions are promising for developing data-driven models with limited knowledge. However, the complex forms of such kernel-based models make it difficult to design the optimal controllers. The design corresponds to solving Hamilton-Jacobi (HJ) equations because their solutions provide optimal controllers. Therefore, the aim of this study is to derive certain kernel-based models for which the HJ equations are solved in an exact sense, which is an extended version of the authors' former work. The HJ equations are decomposed into tractable algebraic matrix equations and nonlinear functions. Solving the matrix equations enables us to obtain the optimal controllers of the model. A numerical simulation demonstrates that kernel-based models and controllers are successfully developed.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAI0002/_p
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@ARTICLE{e105-a_1_1,
author={Yuji ITO, Kenji FUJIMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Kernel-Based Hamilton-Jacobi Equations for Data-Driven Optimal Control: The General Case},
year={2022},
volume={E105-A},
number={1},
pages={1-10},
abstract={Recently, control theory using machine learning, which is useful for the control of unknown systems, has attracted significant attention. This study focuses on such a topic with optimal control problems for unknown nonlinear systems. Because optimal controllers are designed based on mathematical models of the systems, it is challenging to obtain models with insufficient knowledge of the systems. Kernel functions are promising for developing data-driven models with limited knowledge. However, the complex forms of such kernel-based models make it difficult to design the optimal controllers. The design corresponds to solving Hamilton-Jacobi (HJ) equations because their solutions provide optimal controllers. Therefore, the aim of this study is to derive certain kernel-based models for which the HJ equations are solved in an exact sense, which is an extended version of the authors' former work. The HJ equations are decomposed into tractable algebraic matrix equations and nonlinear functions. Solving the matrix equations enables us to obtain the optimal controllers of the model. A numerical simulation demonstrates that kernel-based models and controllers are successfully developed.},
keywords={},
doi={10.1587/transfun.2021EAI0002},
ISSN={1745-1337},
month={January},}
Copier
TY - JOUR
TI - Kernel-Based Hamilton-Jacobi Equations for Data-Driven Optimal Control: The General Case
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1
EP - 10
AU - Yuji ITO
AU - Kenji FUJIMOTO
PY - 2022
DO - 10.1587/transfun.2021EAI0002
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2022
AB - Recently, control theory using machine learning, which is useful for the control of unknown systems, has attracted significant attention. This study focuses on such a topic with optimal control problems for unknown nonlinear systems. Because optimal controllers are designed based on mathematical models of the systems, it is challenging to obtain models with insufficient knowledge of the systems. Kernel functions are promising for developing data-driven models with limited knowledge. However, the complex forms of such kernel-based models make it difficult to design the optimal controllers. The design corresponds to solving Hamilton-Jacobi (HJ) equations because their solutions provide optimal controllers. Therefore, the aim of this study is to derive certain kernel-based models for which the HJ equations are solved in an exact sense, which is an extended version of the authors' former work. The HJ equations are decomposed into tractable algebraic matrix equations and nonlinear functions. Solving the matrix equations enables us to obtain the optimal controllers of the model. A numerical simulation demonstrates that kernel-based models and controllers are successfully developed.
ER -