scholarly journals Unbiased Minimum-Variance Filter for State and Fault Estimation of Linear Time-Varying Systems with Unknown Disturbances

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Fayçal Ben Hmida ◽  
Karim Khémiri ◽  
José Ragot ◽  
Moncef Gossa
Keyword(s):  
Linear Time ◽  
Dynamical Evolution ◽  
Full Rank ◽  
Discrete Systems ◽  
Minimum Variance ◽  
The State ◽  
Fault Estimation ◽  
Time Varying ◽  
Time Varying Systems ◽  
Unknown Disturbances

This paper presents a new recursive filter to joint fault and state estimation of a linear time-varying discrete systems in the presence of unknown disturbances. The method is based on the assumption that no prior knowledge about the dynamical evolution of the fault and the disturbance is available. As the fault affects both the state and the output, but the disturbance affects only the state system. Initially, we study the particular case when the direct feedthrough matrix of the fault has full rank. In the second case, we propose an extension of the previous case by considering the direct feedthrough matrix of the fault with an arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance (UMV) criteria. A numerical example is given in order to illustrate the proposed method.

scholarly journals Control of Linear Time-Varying Systems Using Forward Riccati Equation

1997 ◽  
Vol 119 (3) ◽  
pp. 536-540 ◽  
Author(s):  
Min-Shin Chen ◽  
Chung-yao Kao
Keyword(s):  
Boundary Condition ◽  
Riccati Equation ◽  
State Feedback ◽  
Linear Time ◽  
The State ◽  
State Feedback Control ◽  
Feedback Gain ◽  
Time Varying ◽  
Time Varying Systems ◽  
Future Information

This paper presents a new state feedback control design for linear time-varying systems. In conventional control designs such as the LQ optimal control, the state feedback gain is calculated off-line by solving a Differential Riccati Equation (DRE) backwards with the boundary condition set at some future time. The apparent disad-vantage of using a backward DRE is that future information of the system matrices is required to find the state feedback gain at every time instant. In this paper, an inversion state transformation is applied to the system so that the DRE associated with the transformed system becomes forward in the sense that its boundary condition is set at the initial time of operation (t = t0). As a result, the forward DRE can be calculated on-line without using future information of the system matrices.

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