Reply to “Comments on ‘Robust state estimation for uncertain discrete-time stochastic systems with missing measurements’”

Automatica ◽  
2014 ◽  
Vol 50 (7) ◽  
pp. 1952-1953
Author(s):  
Tong Zhou
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Missing Measurements

On Nonlinear $H_{\infty }$ Filtering for Discrete-Time Stochastic Systems With Missing Measurements

2008 ◽  
Vol 53 (9) ◽  
pp. 2170-2180 ◽  
Author(s):  
Bo Shen ◽  
Zidong Wang ◽  
Huisheng Shu ◽  
Guoliang Wei
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Missing Measurements

scholarly journals Probability-Dependent Static Output Feedback Control for Discrete-Time Nonlinear Stochastic Systems with Missing Measurements

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Wangyan Li ◽  
Guoliang Wei ◽  
Licheng Wang
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Stochastic Systems ◽  
Output Feedback Control ◽  
Upper And Lower Bounds ◽  
Static Output Feedback ◽  
Missing Measurements ◽  
Design Procedures ◽  
Static Output Feedback Control ◽  
Static Output

This paper is devoted to the problems of gain-scheduled control for a class of discrete-time stochastic systems with infinite-distributed delays and missing measurements by utilizing probability-dependent Lyapunov functional. The missing-measurement phenomenon is assumed to occur in a random way, and the missing probability is time varying with securable upper and lower bounds that can be measured in real time. The purpose is to design a static output feedback controller with scheduled gains such that, for the admissible random missing measurements, time delays, and noises, the closed-loop system is exponentially mean-square stable. At last, a simulation example is exploited to illustrate the effectiveness of the proposed design procedures.

A novel cubature statistically linearized Kalman filter for fractional-order nonlinear discrete-time stochastic systems

2017 ◽  
Vol 24 (24) ◽  
pp. 5880-5897 ◽  
Author(s):  
Hamed Torabi ◽  
Naser Pariz ◽  
Ali Karimpour
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Fractional Order ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Taylor Series Expansion ◽  
The State ◽  
Nonlinear Functions ◽  
Measurement Models

In this paper, the state estimation problem for fractional-order nonlinear discrete-time stochastic systems is considered. A new method for the state estimation of fractional nonlinear systems using the statistically linearized method and cubature transform is presented. The fractional extended Kalman filter suffers from two problems. Firstly, the dynamic and measurement models must be differentiable and, secondly, nonlinearity is approximated by neglecting the higher order terms in the Taylor series expansion; by the proposed method in this paper, these problems can be solved using a statistically linearized algorithm for the linearization of fractional nonlinear dynamics and cubature transform for calculating the expected values of the nonlinear functions. The effectiveness of this proposed method is demonstrated through simulation results and its superiority is shown by comparing our method with some other present methods, such as the fractional extended Kalman filter.

Fixed-Interval Kalman Smoother for Non-Square Descriptor Systems with Correlated Noise

2012 ◽  
Vol 433-440 ◽  
pp. 3601-3607
Author(s):  
Hang Wei Tian ◽  
Ying Shi
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Stochastic Systems ◽  
Fixed Interval ◽  
Descriptor Systems ◽  
Correlated Noise ◽  
Filtering Theory ◽  
Numerical Examples ◽  
Kalman Smoother

Based on the classical Kalman filtering theory, the state estimation problem is considered for non-square descriptor discrete time stochastic systems. Under Assumptions 1~3, a fixed-Interval Kalman smoother for non-square descriptor systems with correlated noise is given. Some numerical examples illustrate the effectiveness of the proposed algorithm.

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