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タイトル: L₁ Discretization for Sampled-Data Controller Synthesis via Piecewise Linear Approximation
著者: Kim, Jung Hoon
Hagiwara, Tomomichi  kyouindb  KAKEN_id
著者名の別形: 萩原, 朋道
キーワード: Fast-lifting
L₁ optimal control
piecewise linear approximation
sampled-data systems
発行日: May-2016
出版者: Institute of Electrical and Electronics Engineers Inc. (IEEE)
誌名: IEEE Transactions on Automatic Control
巻: 61
号: 5
開始ページ: 1143
終了ページ: 1157
抄録: This paper develops a new discretization method with piecewise linear approximation for the L₁ optimal controller synthesis problem of sampled-data systems, which is the problem of minimizing the L∞-induced norm of sampled-data systems. We apply fast-lifting on the top of the lifting technique, by which the sampling interval [0, h) is divided into M subintervals with an equal width. The signals on each subinterval are then approximated by linear functions by introducing two types of 'linearizing operators' for input and output, which leads to piecewise linear approximation of sampled-data systems. By using the arguments of preadjoint operators, we provide an important inequality that forms a theoretical basis for tackling the L₁ optimal controller synthesis problem of sampled-data systems more efficiently than the conventional method. More precisely, a mathematical basis for the piecewise linear approximation method associated with the convergence rate is shown through this inequality, and this suggests that the piecewise linear approximation method may drastically outperform the conventional method in the L₁ optimal controller synthesis problem of sampled-data systems. We then provide a discretization procedure of sampled-data systems by which the L₁ optimal controller synthesis problem is converted to the discrete-time l1 optimal controller synthesis problem. Finally, effectiveness of the proposed method is demonstrated through a numerical example.
著作権等: © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
URI: http://hdl.handle.net/2433/235594
DOI(出版社版): 10.1109/TAC.2015.2452815
出現コレクション:学術雑誌掲載論文等

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