New Development for Control Performance Analysis of Continuous-Time and Sampled-Data Systems through Operator Theoretic Approach and Relevant Studies

• Project/Area Number: 15K06138
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Control engineering/System engineering
• Research Institution: Kyoto University
• Principal Investigator: Hagiwara Tomomichi 京都大学, 工学研究科, 教授 (70189463)
• Research Collaborator: Kim Jung Hoon
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: サンプル値系 / むだ時間系 / L∞ノルム / 入力近似 / 核関数近似 / 高速リフティング / 作用素論 / H2ノルム / H2性能 / L∞/L2誘導ノルム / 一般化制御対象の離散化 / 最適制御器 / 関数空間L∞ / 関数空間L2 / 線形行列不等式 / 制御系の性能解析

Outline of Final Research Achievements

This project gave several new results through an operator theoretic approach on the control performance of not only sampled-data systems but also continuous-time finite-dimensional linear time-invariant systems and time-delay systems. For the L∞ induced norm analysis problem, piecewise constant and linear approximation schemes were studied for the input and kernel functions through the fast-lifting approach. Computation methods through finite-dimensional matrices were developed and the convergence orders of the associated approximation errors were clarified. Refined arguments were also given for the case of finite-dimensional linear time-invariant systems. The optimal controller synthesis problem for the L∞ induced norm reduction problem was also tackled through the derivation of a key inequality relevant to operator approximation. Some relevant results on the stability analysis of time-delay systems were also given.

Research Products

• [Journal Article] Extensive theoretical/numerical comparative studies on H2 and generalised H2 norms in sampled-data systems (2017)
  • Author(s): J. H. Kim and T. Hagiwara
  • Journal Title: International Journal of Control Volume: 90
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Upper/Lower Bounds of Generalized H2 Norms in Sampled-Data Systems with Convergence Rate Analysis and Discretization Viewpoint (2017)
  • Author(s): Kim Jung Hoon、Hagiwara Tomomichi
  • Journal Title: Systems & Control Letters Volume: 107 Pages: 28-35
  • DOI: 10.1016/j.sysconle.2017.06.008
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Extensive Theoretical/Numerical Comparative Studies on $H_2$ and Generalised $H_2$ Norms in Sampled-Data Systems (2017)
  • Author(s): J. H. Kim and T. Hagiwara
  • Journal Title: International Journal of Control Volume: 未定
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] L1 discretization for sampled-data controller synthesis via piecewise linear approximation (2016)
  • Author(s): Jung Hoon Kim, Tomomichi Hagiwara
  • Journal Title: IEEE Transactions on Automatic Control Volume: 印刷中 Issue: 5 Pages: 1143-1157
  • DOI: 10.1109/tac.2015.2452815
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Further results on the L1 analysis of sampled-data systems via kernel approximation approach (2016)
  • Author(s): Jung Hoon Kim, Tomomichi Hagiwara
  • Journal Title: International Journal of Control Volume: 印刷中 Issue: 8 Pages: 1684-1697
  • DOI: 10.1080/00207179.2016.1144239
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] L_infinity-Induced Norm Analysis of Sampled-Data Systems via Piecewise Constant and Linear Approximations (2015)
  • Author(s): J. H. Kim and T. Hagiwara
  • Journal Title: Automatica Volume: 51
  • Peer Reviewed
• [Journal Article] Computing the L_infinity-Induced Norm of LTI Systems via Kernel Approximation and Its Comparison with Input Approximation (2015)
  • Author(s): J. H. Kim and T. Hagiwara
  • Journal Title: IET Control Theory & Applications Volume: 9
  • Peer Reviewed
• [Journal Article] Spectrum of Monodromy Operator for a Time-Delay System with Application to Stability Analysis (2015)
  • Author(s): J. H. Kim, T. Hagiwara and K. Hirata
  • Journal Title: IEEE Transactions on Automatic Control Volume: 60
  • Peer Reviewed
• [Presentation] サンプル値系のLinfinity/L2準ハンケル作用素におけるcriticalな境界の特徴付け (2018)
  • Author(s): 稲井顕，萩原朋道，金正勳
  • Organizer: Ｈ29年度SICE関西支部・ISCIE若手研究発表会
• [Presentation] 多出力サンプル値系のLinfinity/L2準ハンケル作用素におけるcriticalな境界の特徴付け (2018)
  • Author(s): 稲井顕，萩原朋道，金正勳
  • Organizer: 計測自動制御学会第５回制御部門マルチシンポジウム
• [Presentation] サンプル値系における$L_\infty/L_2$準ハンケルノルムの解析 (2017)
  • Author(s): 稲井顕，萩原朋道，金正勳
  • Organizer: 第4回計測自動制御学会制御部門マルチシンポジウム
  • Place of Presentation: 岡山大学 （岡山県岡山市）
  • Year and Date: 2017-03-06
• [Presentation] Kernel Approximation Approach to the L1 Optimal Sampled-Data Controller Synthesis Problem (2017)
  • Author(s): J. H. Kim and T. Hagiwara
  • Organizer: 20th IFAC World Congress
  • Int'l Joint Research
• [Presentation] Characterization of Quasi Linfinity/L2 Hankel Norms of Sampled-Data Systems (2017)
  • Author(s): A. Inai, T. Hagiwara and J. H. Kim
  • Organizer: 20th IFAC World Congress
  • Int'l Joint Research
• [Presentation] A Discretization Approach to the Analysis of yet Another H2 Norm of LTI Sampled-Data Systems (2017)
  • Author(s): J. H. Kim and T. Hagiwara
  • Organizer: 56th IEEE Conference on Decision and Control
  • Int'l Joint Research
• [Presentation] 連続時間線形周期時変系のLinfinity/L2ハンケルノルムとその性質 (2017)
  • Author(s): 檜垣周佑，萩原朋道，金正勳
  • Organizer: 第61回システム制御情報学会研究発表講演会
• [Presentation] サンプル値系の$L_\infty/L_2$準ハンケルノルムの計算法 (2017)
  • Author(s): 稲井顕，萩原朋道，金正勳
  • Organizer: 平成28年度SICE関西支部・ISCIE若手研究発表会
  • Place of Presentation: 大阪大学 （大阪府吹田市）
• [Presentation] The $L_\infty/L_2$ Hankel Norm of Sampled-Data Systems (2016)
  • Author(s): T. Hagiwara, A. Inai and J. H. Kim
  • Organizer: 2016 IEEE 55th Conference on Decision and Control
  • Place of Presentation: Las Vegas （アメリカ）
  • Year and Date: 2016-12-12
• [Presentation] A Study on Discretization Approach to the $L_\infty/L_2$ Optimal Control Synthesis Problem in Sampled-Data Systems (2016)
  • Author(s): J. H. Kim and T. Hagiwara
  • Organizer: 2016 IEEE 55th Conference on Decision and Control
  • Place of Presentation: Las Vegas （アメリカ）
  • Year and Date: 2016-12-12
• [Presentation] サンプル値系における $L_\infty/L_2$ ハンケル作用素とそのノルムに関する考察 (2016)
  • Author(s): 稲井顕，金正勳，萩原朋道
  • Organizer: 第60回システム制御情報学会研究発表講演会
  • Place of Presentation: 京都テルサ （京都府京都市）
  • Year and Date: 2016-05-25
• [Presentation] Computation of the Induced Norm from L_2 to L_infinity in SISO Sampled-Data Systems: Discretization Approach with Convergence Rate Analysis (2015)
  • Author(s): J. H. Kim and T. Hagiwara
  • Organizer: 2015 IEEE Conference on Decision and Control
  • Place of Presentation: Osaka, Japan
  • Year and Date: 2015-12-15
• [Presentation] L_1 Analysis of LTI Systems via Piecewise Higher-Order Approximation (2015)
  • Author(s): Y. W. Choi, J. H. Kim and T. Hagiwara
  • Organizer: 2015 IEEE Multi-Conference on Systems and Control
  • Place of Presentation: Sydney, Australia
  • Year and Date: 2015-09-21
• [Presentation] Kernel Approximation Approach to the L_1 Analysis of Sampled-Data Systems (2015)
  • Author(s): J. H. Kim and T. Hagiwara
  • Organizer: 2015 European Control Conference
  • Place of Presentation: Linz, Austria
  • Year and Date: 2015-07-15
• [Presentation] Induced Norm from L_2 to L_infinity in SISO Sampled-Data Systems (2015)
  • Author(s): J. H. Kim and T. Hagiwara
  • Organizer: 2015 American Control Conference
  • Place of Presentation: Chicago, USA
  • Year and Date: 2015-07-01