Robust Nonlinear H∞ Control Design via Stable Manifold Method

Robust Nonlinear H∞ Control Design via Stable Manifold Method

This paper proposes a systematic numerical method for designing robust nonlinear H∞ controllers without a priori lower-dimensional approximation with respect to solutions of the Hamilton-Jacobi equations. The method ensures the solutions are globally calculated with arbitrary accuracy in terms of th...

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Main Authors: Yoshiki Abe, Gou Nishida, Noboru Sakamoto, Yutaka Yamamoto
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/198380
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spelling doaj-c78f79643a86447c8f45de1a44e2a22f2020-11-24T23:02:29ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/198380198380Robust Nonlinear H∞ Control Design via Stable Manifold MethodYoshiki Abe0Gou Nishida1Noboru Sakamoto2Yutaka Yamamoto3Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, JapanDepartment of Mechanical and Environmental Informatics, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, 2-12-1 W8-1, O-okayama, Meguro-ku, Tokyo 152-8552, JapanDepartment of Mechatronics, Faculty of Science and Engineering, Nanzan University, 18 Yamazato-cho, Shyowa-ku, Nagoya 466-8673, JapanDepartment of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, JapanThis paper proposes a systematic numerical method for designing robust nonlinear H∞ controllers without a priori lower-dimensional approximation with respect to solutions of the Hamilton-Jacobi equations. The method ensures the solutions are globally calculated with arbitrary accuracy in terms of the stable manifold method that is a solver of Hamilton-Jacobi equations in nonlinear optimal control problems. In this realization, the existence of stabilizing solutions of the Hamilton-Jacobi equations can be derived from some properties of the linearized system and the equivalent Hamiltonian system that is obtained from a transformation of the Hamilton-Jacobi equation. A numerical example is shown to validate the design method.http://dx.doi.org/10.1155/2015/198380
collection DOAJ
language English
format Article
sources DOAJ
author Yoshiki Abe
Gou Nishida
Noboru Sakamoto
Yutaka Yamamoto
spellingShingle Yoshiki Abe
Gou Nishida
Noboru Sakamoto
Yutaka Yamamoto
Robust Nonlinear H∞ Control Design via Stable Manifold Method
Mathematical Problems in Engineering
author_facet Yoshiki Abe
Gou Nishida
Noboru Sakamoto
Yutaka Yamamoto
author_sort Yoshiki Abe
title Robust Nonlinear H∞ Control Design via Stable Manifold Method
title_short Robust Nonlinear H∞ Control Design via Stable Manifold Method
title_full Robust Nonlinear H∞ Control Design via Stable Manifold Method
title_fullStr Robust Nonlinear H∞ Control Design via Stable Manifold Method
title_full_unstemmed Robust Nonlinear H∞ Control Design via Stable Manifold Method
title_sort robust nonlinear h∞ control design via stable manifold method
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description This paper proposes a systematic numerical method for designing robust nonlinear H∞ controllers without a priori lower-dimensional approximation with respect to solutions of the Hamilton-Jacobi equations. The method ensures the solutions are globally calculated with arbitrary accuracy in terms of the stable manifold method that is a solver of Hamilton-Jacobi equations in nonlinear optimal control problems. In this realization, the existence of stabilizing solutions of the Hamilton-Jacobi equations can be derived from some properties of the linearized system and the equivalent Hamiltonian system that is obtained from a transformation of the Hamilton-Jacobi equation. A numerical example is shown to validate the design method.
url http://dx.doi.org/10.1155/2015/198380
work_keys_str_mv AT yoshikiabe robustnonlinearhcontroldesignviastablemanifoldmethod
AT gounishida robustnonlinearhcontroldesignviastablemanifoldmethod
AT noborusakamoto robustnonlinearhcontroldesignviastablemanifoldmethod
AT yutakayamamoto robustnonlinearhcontroldesignviastablemanifoldmethod
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