Matrix Riccati Equations in Systems and Control Theory
| Project/Area Number |
05650417
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
計測・制御工学
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
KANO Hiroyuki Tokyo Denki University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (00246654)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIMURA Toshimitsu Tokyo Engineering University, Faculty of Engineering, Professor, 工学部, 教授 (30150048)
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| Project Period (FY) |
1993 – 1994
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| Project Status |
Completed (Fiscal Year 1994)
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| 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)
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| Keywords | Matrix Riccati equations / Optimal control and filtering / H_* control / Stabilizing solutions / ロバスト制御 |
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| 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.
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Report
(3 results)
Research Products
(5 results)
