Strong stability of quasi-affine transforms of contraction semigroups and the steady-state riccati equation

1985 ◽  
Vol 45 (3) ◽  
pp. 397-406 ◽  
Author(s):  
N. Levan
Keyword(s):  
Steady State ◽  
Riccati Equation ◽  
Strong Stability ◽  
Contraction Semigroups ◽  
Affine Transforms

A Fast Computational Approach in Optimal Distributed-Parameter State Estimation

1983 ◽  
Vol 105 (1) ◽  
pp. 1-10 ◽  
Author(s):  
K. Watanabe ◽  
M. Iwasaki
Keyword(s):  
Steady State ◽  
Riccati Equation ◽  
Computation Time ◽  
Computational Approach ◽  
Distributed Parameter ◽  
Kutta Method ◽  
Step Size ◽  
Runge Kutta Method ◽  
Operator Riccati Equation ◽  
Runge Kutta

A fast computational approach is considered for solving of a time-invariant operator Riccati equation accompanied with the optimal steady-state filtering problem of a distributed-parameter system. The partitioned filter with the effective initialization is briefly explained and some relationships between its filter and the well-known Kalman-type filter are shown in terms of the Meditch-type fixed-point smoother in Hilbert spaces. Then, with the aid of these results the time doubling algorithm is proposed to solve the steady-state solution of the operator Riccati equation. Some numerical examples are included and a comparison of the computation time required by the proposed method is made with other algorithms—the distributed partitioned numerical algorithm, and the Runge-Kutta method. It is found that the proposed algorithm is approximately from 40 to 50 times faster than the classical Runge-Kutta method with constant step-size for the case of 9th order mode Fourier expansion.

scholarly journals Synthesis of lunberger stochastic observer for estimation of the grinding operation state

2018 ◽  
Vol 224 ◽  
pp. 01133 ◽  
Author(s):  
Sergey Bratan ◽  
Stanislav Roshchupkin
Keyword(s):  
Steady State ◽  
Riccati Equation ◽  
Real Time ◽  
The State ◽  
Technological System ◽  
Steady State Mode ◽  
Estimation Errors ◽  
Optimal Estimates

The technique of constructing Lunberger stochastic observer for the operation of circular external grinding is considered in the article, which makes it possible to obtain optimal estimates of the output parameters of the technological system. To build Lunberger stochastic observer, a program has been developed that allows solving the Riccati equation of the object and the filter. The calculation of the Kalman-Buсy filter coefficients for the steady-state mode of the process of grinding the camshaft journal is performed. This allows us to evaluate the state of the system in real time, and even in the case of measuring only one coordinate, the filter gives estimates of all coordinates, and the maximum estimation errors do not exceed 10%.

scholarly journals On the Convergence of the Modified Riccati Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Target Tracking ◽  
Riccati Equation ◽  
Detection Probability ◽  
Iterative Algorithms ◽  
Iterative Solution ◽  
Steady State Solution ◽  
Critical Value ◽  
Solution Algorithm

The modified Riccati equation arises in the implementation of Kalman filter in target tracking under measurement uncertainty and it cannot be transformed into an equation of the form of the Riccati equation. An iterative solution algorithm of the modified Riccati equation is proposed. A method is established to decide when the proposed algorithm is faster than the classical one. Both algorithms have the same behavior: if the system is stable, then there exists a steady-state solution, while if the system is unstable, then there exists a critical value of the measurement detection probability, below which both iterative algorithms diverge. It is established that this critical value increases in a logarithmic way as the system becomes more unstable.

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