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Application of global searching algorithms for nonlinear control system designing

Research Project

Project/Area Number 10650428
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Control engineering
Research InstitutionNagoya University

Principal Investigator

HOSOE Shigeyuki  Nagoya University, Engineering, Professor, 工学研究科, 教授 (50023198)

Co-Investigator(Kenkyū-buntansha) TUAN Hoang Duong  Nagoya University, Engineering, Associate Professor, 工学部, 助教授 (60262854)
MIYAZAKI Takashi  Nagoya University, Engineering, Research Assistant, 工学研究科, 助手 (30252274)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1999: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1998: ¥2,400,000 (Direct Cost: ¥2,400,000)
KeywordsLinear Matrix Inequality / Bilinear Matrix Inequality / Nonconvex function / Global optimization / Gain Scheduling / Robust control / d.c. structure / Spin Avoidance / 線形行列不等式 LMI / 双線形行列不等式 BMI
Research Abstract

Bilinear Matrix Inequality (BMI), an extension of LMI, is attracting a considerable attention as a powerful tool for designing nonlinear control systems and robust control systems with structured uncertainties.
As opposed to LMI, BMI is non-convex and its computation is usually very difficult. Therefore, to find algorithms with rapid convergence with guarantying global optimality is extremely important. For some BMIs, however, there are problems for which long computational time is unavoidable no matter what algorithm is used. In such a case, admitting some conservatism, to use LMI algorithm after converting BMI into LMI is very practical.
Standing on the above viewpoint, the following studies are carried out. (i) Extension of LMI technique. (ii) Reduction of BMI into LMI. (iii) Derivation of BMI solving algorithms. (iv) Applications to automobile control systems.
The following results are obtained. A new LMI algorithm has been derived for HィイD2∞ィエD2 control problem for descriptor systems. Also, HィイD2∞ィエD2 control problems with time-domain constraints and multi-rate sampled data HィイD2∞ィエD2 control problems have been solved within LMIs. Concerning to the reduction of BMI into LMI, an algorithm has been proposed for parameterized LMI (PLMI) problems. For BMI, observing that BMi has a structure of d.c. constraints (difference of convex functions), a new branch and bound algorithm has been proposed. Finally these results have been applied to automobile controls.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] E. Ono, S. Hosoe, H. D. Tuan and S. Doi: "Bifurcation in Vehicle Dynamics and Robust Front Wheel Steering Control"IEEE Trans. on Control Systems Technology. 6-3. 412-420 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. D. Tuan and S. Hosoe: "On Robust H∞ Control for Nonlinear Discrete and Sampled-Data Systems"IEEE Trans. on Automatic Control. 43-5. 715-718 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. D. Tuan and S. Hosoe: "On linear robust H∞ controls for a class of nonlinear singularly perturbed systems"Automatica. 35-4. 735-739 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 小野,細江,浅野,菅井,土居: "ゲインスケジュールドH∞制御による車両運動のロバスト安定化"計測自動制御学会論文集. 35-3. 393-400 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 宮崎,細江: "無限遠点に零点を持つディスクリプタシステムに対するJスペクトル分と一般化リカッチ方程式"計測自動制御学会論文集. 35-6. 723-731 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.D.Tuan,細江,P.Apkarian: "D.C.optimization in robust control synthesis"オペレーションズ・リサーチ. 44-5. 247-252 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] E. Ono, S. Hosoe, H.D. Tuan and S. Doi: "Bifurcation in Vehicle Dynamics and Robust Front Wheel Steering Control"IEEE Trans. in Control Systems Technology. Vol. 6-3. 412-420 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. D. Tuan and S. Hosoe: "On robust HィイD2∞ィエD2 controls for a class of nonlinear singularly perturbed systems"Automatica. Vol.43-5. 715-718 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H. D. Tuan and S. Hosoe: "On linear robust HィイD2∞ィエD2 controls for a class of nonlinear singularly pertuebed systems"Automatica. Vol.35-4. 735-739 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Ono, Hosoe, Asano, Sugai, Doi: "Robust Stabilization of the Vehicle Dynamics by Gain-Scheduled HィイD2∞ィエD2 control"Trans. of the Society of Instrument and Control Engineers. Vol.35-3. 393-400 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. MIyazaki and S. Hosoe: "J-Spectral Factorization and Generalized Algebraic Equation for Descriptor Systems with Infinite Zeros"Trans. of the Society of Instrument and Control Engineers. Vol.35-6. 723-731 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H.D. Tuan, S. Hosoe and P. Aplkarian: "D. C. Optimization in Robust Control Synthesis"Operation Researches. Vol.44-5. 247-252

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] E.Ono.,S.Hosoe,H.D.Tuan and S.Doi: "Bifurcation in Vehicle Dynamics and Robust Front Wheel Steering Control"IEEE Trans. on Control Systems Technology. 6-3. 412-420 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.D.Tuan and S.Hosoe: "On Robust H∞ Control for Nonlinear Discrete and Sampled-Data Systems"IEEE Trans. on Automatic Control. 43-5. 715-718 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.D.Tuan and S.Hosoe: "On linear robust H∞ controls for a class of nonlinear singularly perturbed systems"Automatica. 35-4. 735-739 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 小野,細江,浅野,菅井,土居: "ゲインスケジュールドH∞制御による車両運動のロバスト安定化"計測自動制御学会論文集. 35-3. 393-400 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 宮崎,細江: "無限遠点に零点を持つディスクリプタシステムに対するJスペクトル分と一般化リカッチ方程式"計測自動制御学会論文集. 35-6. 723-731 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] H.D.Tuan,細江,P,Apkarian: "D.C.optimization in robust control synthesis"オペレーションズ・リサーチ. 44-5. 247-252 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] E.Ono,S.Hosoe,H.D.Tuan and S.Doi: "Bifurcation in Vehicle Dynamics and Robust Front Wheel Steering Control" IEEE Trans.on Control Systems Technology. 6-3. 412-420 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Hosoe: "LMI Approach to H_∞ Control Problem with Time Domain Constraints" IEEE Trans.on Automatic Control. 43-8. 1128-1132 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 宮崎,武山,細江: "ディスクリプタシステムに対するH∞制御問題のLMIによる解法" 計測自動制御学会論文集. 34-8. 1013-1018 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] P.Apkarian,H.D.Tuan: "Robust control via concave optimization : local and gloval algorithms" Proc.of 37th IEEE Conf.on Decision and Control. 3855-3860 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.D.Tuan,P.Apkarian: "Relaxazation of parameterized LMIs with control application" International J.of Nonlinear Controls. 9. 59-84 (1999)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2021-04-07  

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