Project/Area Number  03650516 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
000264

Research Institution  The University of Tokyo 
Principal Investigator 
OKANO Yasuhiko The University of Tokyo, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30011092)

CoInvestigator(Kenkyūbuntansha) 
OKAYA Katsunori The University of Tokyo, Faculty of Engineering, Instructor, 工学部, 助手 (80134493)
INOUE Toshio The University of Tokyo, Faculty of Engineering, Professor, 工学部, 教授 (80010742)
NONAKA Michio The University of Tokyo, Faculty of Engineering, Instructor, 工学部, 助手 (70010981)

Project Fiscal Year 
1991 – 1992

Project Status 
Completed(Fiscal Year 1992)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1992 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1991 : ¥1,200,000 (Direct Cost : ¥1,200,000)

Keywords  extended Kalman Filter / state estimation / Riccati equation / optimal sampling / Lorenz system / chaos / LQG control / Hinfinity control / 拡張カルマンフィルタ / 状態推定 / リカッチ方程式 / 最適サンプリング / カオス / LQG制御 / H∞制御 / 誤差共分散行列 / strange attractor / 共役勾配法 / discrete vortex simulation / カルマンフィルタ / 非線形 
Research Abstract 
The switching mode enhanced extended Kalman(SEEK) filter algorithm has been developed to estimate strongly nonlinear and noisy dynamical systems. The SEEK algorithm is based on optimally selecting the observation matrix so as to ensure the convergence of the estimation error covariance matrix is maximized. The basic concept has been outlined using a second order linear system and successfully verified by numerical demonstrations. Then the SEEK filter algorithm has been applied to estimate the Lorenz system with superimposed Gaussian white noise. The SEEK filter has returned good estimates of this chaotic system though the conventional extended Kalman filter absolutely failed to obtain accurate state estimates. The optimization algorithm for selecting the optimal sampling mode has been developed and applied to estimate the Lorenz system with a switched parameter. We regard this demonstration as convincing evidence of the power of the SEEK filter as an accurate estimator of the state variables even for strongly nonlinear systems such as this particular relization of the Lorenz system. The SEEK algorithm has also been applied to identify evolving large structure in flows accompanied with microstructure diffusion in a discrete vortex simulation. The SEEK filter achieved accurate estimation even in a high level noisy environment. Then only diagonal elements of the Jacobian matrix have been found to be dominant in applying the SEEK algorithm to the discrete vortex simulation. This evidence should be quite useful to reduce the calculation time in a large code estimation. Then, from the viewpoint of applicability of Kalman filtering technology to control practices, therefore, control performances have been compared among the cases of conventional PID, LQG and Hinfinity controls, supposing a typical transfer function of the control object,which is certainly common to powder processes.
