Matrix Riccati Equations in Systems and Control Theory
Project/Area Number  05650417 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
計測・制御工学

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

CoInvestigator(Kenkyūbuntansha) 
NISHIMURA Toshimitsu Tokyo Engineering University, Faculty of Engineering, Professor, 工学部, 教授 (30150048)

Project Fiscal Year 
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)

Keywords  Matrix Riccati equations / Optimal control and filtering / H_* control / Stabilizing solutions / マトリクス・リッカチ方程式 / 最適推定制御 / H_∞制御 / 可安定解 / ロバスト制御 
Research Abstract 
(1) Theoretical Analysis : Algebraic matrix Riccati equations for continuoustime systems of the form FP+PF^TPRP+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_1gamma^<2>H^T_H_2, and gamma* reduces to the wellknown 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, antistabilizing solutions together with all the other solutions, thereby clarified the lattice structure of solutions. Some of the results are extended to the cases of discretetime systems and periodically timevarying systems. Then we derived necessary conditions for the existence of nonnegative and positivedefinite 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 eigenvalueeigenvector 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 socalled modern control theory in the last 30 years. It focuses on the equations in LQG control problems for continuoustime systems covering from the theories to applications, with additional chapters on H_* control problems as well as discretetime 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
(4results)
Research Output
(5results)