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Matrix Riccati Equations in Systems and Control Theory

Research Project

Project/Area Number 05650417
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 計測・制御工学
Research InstitutionTokyo Denki University

Principal Investigator

KANO Hiroyuki  Tokyo Denki University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (00246654)

Co-Investigator(Kenkyū-buntansha) NISHIMURA Toshimitsu  Tokyo Engineering University, Faculty of Engineering, Professor, 工学部, 教授 (30150048)
Project Period (FY) 1993 – 1994
Project Status Completed (Fiscal Year 1994)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1994: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1993: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsMatrix Riccati equations / Optimal control and filtering / H_* control / Stabilizing solutions / ロバスト制御
Research Abstract

(1) Theoretical Analysis : Algebraic matrix Riccati equations for continuous-time systems of the form FP+PF^T-PRP+Q=0, where R=R^T and Q=Q^T<greater than or equal>0, are studied. Both theoretical analysis and numerical experiments are performed. In the case of H_* control problems, the matrix R in general takes the form R=H^T_H_1-gamma^<-2>H^T_H_2, and gamma* reduces to the well-known LQG case with R<greater than or equal>0. Here we studied in detail the other limit case of gamma*0, namely R<less than or equal>0. Necessary and sufficient conditions are derived for the existence of stabilizing solutions, anti-stabilizing solutions together with all the other solutions, thereby clarified the lattice structure of solutions. Some of the results are extended to the cases of discrete-time systems and periodically time-varying systems.
Then we derived necessary conditions for the existence of nonnegative- and positive-definite stabilizing solutions for general case of R.These conditions coincide with necessary and sufficient conditions when applied to the above cases of R<greater than or equal>0 and R<less than or equal>0. But the sufficiency proofs remain unsolved as a future problem. In these studies, we developed several softwares for computing solutions by both eigenvalue-eigenvector method and Newton's method, also for computing H_* norms in the existence con
(2) Publication of Book : We prepared a manuscript for a book, which compiles the results on Riccati equations developed in the so-called modern control theory in the last 30 years. It focuses on the equations in LQG control problems for continuous-time systems covering from the theories to applications, with additional chapters on H_* control problems as well as discrete-time systems. We assumed as readers researchers, students and engineers in systems and control area. This will be published as part of the 'Systems and Information' series of the Institute of Systems, Control and Information Engineers of Japan.

Report

(3 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • Research Products

    (5 results)

All Other

All Publications (5 results)

  • [Publications] H. Kano: "Nonnegative-Definite Solutions of Algebraic Matrix Riccati Equations with Nonnegative-Definite Quadratic and Constant Terms" Systems and Networks : Mathematical Theory and Applications. 2. 265-268 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 西村敏充: "マトリクス・リッカチ方程式の基礎と応用" 朝倉書店(予定),

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] H.Kano and T.Nishimura.: "Nonnegative-Definite Solutions of Algebraic Matrix Riccati Equations with Nonnegative-Definite Quadratic and Constant Terms" Systems and Networks : Mathematical Therory and Applications. vol.2. 265-268 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] T.Nishimura and H.Kano: Mathematical Theory and Applications of Matrix Riccati Equations (in Japanese). Asakura Publishing Co. (in preparation),

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] H.Kano and T.Nishimura: "Nonnegative-Definite Solutions of Algebraic Matrix Riccati Eguations with Nonnegative-Definite Quadratic and Constant Terms" Systems and Networks:Mathematical Theory and Applications. 2. 265-268 (1994)

    • Related Report
      1994 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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