Analisis Kestabilan Kalman Filter Sistem Singular dengan Pendekatan Deterministik

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Budi Rudianto
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Riccati Equation ◽  
Discrete Time ◽  
Simple Structure ◽  
Descriptor Systems ◽  
Deterministic Approach ◽  
Optimal Form

Makalah ini membahas Kalman filter dan Persamaan Aljabar Ricatti (PAR) untuk waktu diskrit. Lebih lanjut, sistem deskriptor varian waktu ditampilkan dalm bentuk formulasi umum. Pendekatan deterministik digunakan untuk menentukan bentuk optimum menjadi formulasi 9-block. Pernyataan 9-block selain menyatakan tahapan kondisi ruang, juga menampilkan struktur sederhana yang menarik dan simetris. Kemudian, kami akan menunjukkan bahwa Persamaan Aljabar Ricatti (PAR) memiliki semidefinit dan menstabilkan sistem.   In this paper will discuss the Kalman filter and Riccati equation for discrete-time. Furthermore, time-variant descriptor systems presented in a common formulation. Deterministic approach used to determine the optimal form into the formulation "9-block". The expression "9-block", besides stating stages pending state space, also presents a simple structure that is interesting and symmetrical. And then, we will show that the Aljabar Riccati Eqution has a stabilizing semi-definit.

THE LINEAR QUADRATIC DYNAMIC GAME FOR DISCRETE-TIME DESCRIPTOR SYSTEMS

2003 ◽  
Vol 05 (04) ◽  
pp. 361-374
Author(s):  
HUA XU ◽  
HIROAKI MUKAIDANI
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Dynamic Game ◽  
Descriptor Systems ◽  
Linear Feedback ◽  
Space System ◽  
Linear Quadratic ◽  
Reduced Order ◽  
State Space System ◽  
Zero Sum

The linear quadratic zero-sum dynamic game for discrete time descriptor systems is considered. A method, which involves solving a linear quadratic zero-sum dynamic game for a reduced-order discrete time state space system, is developed to find the linear feedback saddle-point solutions of the problem. Checkable conditions, which are described in terms of two dual algebraic Riccati equations and a Hamiltonian matrix, are given such that the linear quadratic zero-sum dynamic game for the reduced-order discrete time state space system is available. Sufficient conditions for the existence of the solutions are obtained. In contrast with the dynamic game in state space systems, the dynamic game in descriptor systems admits uncountably many linear feedback saddle-point solutions. All these solutions have the same existence conditions and achieve the same value of the dynamic game.

scholarly journals Kalman Filter Riccati Equation for the Prediction, Estimation, and Smoothing Error Covariance Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Nicholas Assimakis ◽  
Maria Adam
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
Discrete Time ◽  
Prediction Error ◽  
Estimation Error ◽  
Riccati Equations ◽  
Covariance Matrices ◽  
Linear Estimation ◽  
Solution Algorithms ◽  
Error Covariance

The classical Riccati equation for the prediction error covariance arises in linear estimation and is derived by the discrete time Kalman filter equations. New Riccati equations for the estimation error covariance as well as for the smoothing error covariance are presented. These equations have the same structure as the classical Riccati equation. The three equations are computationally equivalent. It is pointed out that the new equations can be solved via the solution algorithms for the classical Riccati equation using other well-defined parameters instead of the original Kalman filter parameters.

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