Controller designs with symbolic numeric computations.

• Project/Area Number: 23540139
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Yamaguchi University
• Principal Investigator: KITAMOTO TAKUYA 山口大学, 教育学部, 教授 (30241780)
• Co-Investigator(Kenkyū-buntansha): KISHIWAGI Yoshimi 山口大学, 経育学部, 教授 (00152637)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 数値数式融合 / 数式処理 / 制御系設計 / 数値数式融合算法 / 冪級数展開 / Pade近似 / 数値数式融合計算

Outline of Final Research Achievements

Usually, symbolic computations in a computer algebra system do not permit any numerical errors, and floating point arithmetic and power series computations are not allowed. Therefore, so far, applications of symbolic computations for controller designs has been limited.
In this study, we apply symbolic computations to controller designs, utilizing power series computations. We approximate a mathematical expression with its power series expression. It is possible to perform arithmetic operations such as additions, subtractions, multiplications and divisions on power series, which enable us flexible symbolic computations.

Research Products

• [Journal Article] On the Computation of the Determinant of a Generalized Vandermonde Matrix (2014)
  • Author(s): Takuya Kitamoto
  • Journal Title: Lecture Notes in Computer Science Volume: 8660 Pages: 242-255
  • DOI: 10.1007/978-3-319-10515-4_18
  • ISBN: 9783319105147, 9783319105154
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Multivariate Pade approximation using Quantifier Elimination (2015)
  • Author(s): Takuya Kitamoto
  • Organizer: ATCM2015
  • Place of Presentation: Leshan, China
  • Year and Date: 2015-12-16
  • Int'l Joint Research
• [Presentation] Pade近似の制御系設計への応用について (2015)
  • Author(s): 北本卓也
  • Organizer: 数式処理とその周辺分野の研究 － Computer Algebra and Related Topics
  • Place of Presentation: 京都大学（京都府, 京都市）
  • Year and Date: 2015-12-02
• [Presentation] 多変数のPade近似について (2013)
  • Author(s): 北本卓也
  • Organizer: 第２２回日本数式処理学会大会
  • Place of Presentation: 防衛大学校（神奈川県横須賀市）
• [Presentation] Applications of CAS to analyze the step response of a system with parameters (2012)
  • Author(s): T. Kitamoto
  • Organizer: The 17th Asian Technology Conference in Mathematics
  • Place of Presentation: Bangkok(Thailand)
• [Presentation] H∞を用いた制御系設計について (2011)
  • Author(s): 北本 卓也
  • Organizer: 数式処理 － その研究と目指すもの
  • Place of Presentation: 京都大学数理解析研究所, 京都市
• [Presentation] 数式処理の制御系設計への応用について (2011)
  • Author(s): 北本 卓也
  • Organizer: 数式処理研究の新たな発展
  • Place of Presentation: 京都大学数理解析研究所, 京都市