On periodic and bounded solutions of the operator Riccati equation

1993 ◽  
Vol 45 (2) ◽  
pp. 255-259
Author(s):  
A. Ya. Dorogovtsev
Keyword(s):  
Riccati Equation ◽  
Bounded Solutions ◽  
Operator Riccati Equation

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.

F-reduction of the operator Riccati equation for hereditary differential systems

Automatica ◽  
1978 ◽  
Vol 14 (4) ◽  
pp. 385-395 ◽  
Author(s):  
M.C. Delfour ◽  
E.B. Lee ◽  
A. Manitius
Keyword(s):  
Riccati Equation ◽  
Differential Systems ◽  
Operator Riccati Equation

scholarly journals Bound and periodic solutions of the Riccati equation in Banach space

1995 ◽  
Vol 8 (2) ◽  
pp. 195-200 ◽  
Author(s):  
A. Ya. Dorogovtsev ◽  
T. A. Petrova
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Nonlinear Differential Equation ◽  
Periodic Process ◽  
Bounded Solutions ◽  
The Right

An abstract, nonlinear, differential equation in Banach space is considered. Conditions are presented for the existence of bounded solutions of this equation with a bounded right side, and also for the existence of stationary (periodic) solutions of this equation with a stationary (periodic) process in the right side.

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