Abstract
A recursive robust H∞ filtering algorithm is newly proposed for the discrete time uncertain linear system subject to the energy constraint called sum quadratic constraint (SQC). A set valued estimation approach will be used to tackle the given problem. To this end, by combining an SQC on the H∞ norm condition of the error dynamics and an inequality relationship between the uncertainty input and output, we obtain an augmented SQC and then formulate the robust H∞, filtering problem as the one of finding the set of estimates satisfying this constraint. The solutions will be given in terms of ellipsoids whose centers are the minimums of the indefinite quadratic function defined by the augmented SQC. The Krein space estimation theory will be utilized to efficiently deal with the minimization problem of the indefinite quadratic function and it is shown that the robust H∞ filter turns out to be just the special form of Krein space Kalman filter. The proposed robust filter has basically the same recursive structure as the information form of Kalman filter and therefore demands less computational burdens for the implementation. Numerical examples will be given to verify that the proposed filter guarantees the robustness in the presence of parametric uncertainties and its bounding ellipsoidal sets of filtered estimates always contain true states.
| Original language | English |
|---|---|
| Pages (from-to) | 5182-5187 |
| Number of pages | 6 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| Volume | 5 |
| Publication status | Published - 2004 Dec 1 |
| Event | 2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas Duration: 2004 Dec 14 → 2004 Dec 17 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization
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Recursive robust H∞ filtering within the framework of set-valued estimation. / Ra, Won Sang; Jin, Seung Hee; Yoon, Tae Sung; Park, Jin Bae.
In: Proceedings of the IEEE Conference on Decision and Control, Vol. 5, 01.12.2004, p. 5182-5187.Research output: Contribution to journal › Conference article
TY - JOUR
T1 - Recursive robust H∞ filtering within the framework of set-valued estimation
AU - Ra, Won Sang
AU - Jin, Seung Hee
AU - Yoon, Tae Sung
AU - Park, Jin Bae
PY - 2004/12/1
Y1 - 2004/12/1
N2 - A recursive robust H∞ filtering algorithm is newly proposed for the discrete time uncertain linear system subject to the energy constraint called sum quadratic constraint (SQC). A set valued estimation approach will be used to tackle the given problem. To this end, by combining an SQC on the H∞ norm condition of the error dynamics and an inequality relationship between the uncertainty input and output, we obtain an augmented SQC and then formulate the robust H∞, filtering problem as the one of finding the set of estimates satisfying this constraint. The solutions will be given in terms of ellipsoids whose centers are the minimums of the indefinite quadratic function defined by the augmented SQC. The Krein space estimation theory will be utilized to efficiently deal with the minimization problem of the indefinite quadratic function and it is shown that the robust H∞ filter turns out to be just the special form of Krein space Kalman filter. The proposed robust filter has basically the same recursive structure as the information form of Kalman filter and therefore demands less computational burdens for the implementation. Numerical examples will be given to verify that the proposed filter guarantees the robustness in the presence of parametric uncertainties and its bounding ellipsoidal sets of filtered estimates always contain true states.
AB - A recursive robust H∞ filtering algorithm is newly proposed for the discrete time uncertain linear system subject to the energy constraint called sum quadratic constraint (SQC). A set valued estimation approach will be used to tackle the given problem. To this end, by combining an SQC on the H∞ norm condition of the error dynamics and an inequality relationship between the uncertainty input and output, we obtain an augmented SQC and then formulate the robust H∞, filtering problem as the one of finding the set of estimates satisfying this constraint. The solutions will be given in terms of ellipsoids whose centers are the minimums of the indefinite quadratic function defined by the augmented SQC. The Krein space estimation theory will be utilized to efficiently deal with the minimization problem of the indefinite quadratic function and it is shown that the robust H∞ filter turns out to be just the special form of Krein space Kalman filter. The proposed robust filter has basically the same recursive structure as the information form of Kalman filter and therefore demands less computational burdens for the implementation. Numerical examples will be given to verify that the proposed filter guarantees the robustness in the presence of parametric uncertainties and its bounding ellipsoidal sets of filtered estimates always contain true states.
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M3 - Conference article
AN - SCOPUS:14544277164
VL - 5
SP - 5182
EP - 5187
JO - Proceedings of the IEEE Conference on Decision and Control
JF - Proceedings of the IEEE Conference on Decision and Control
SN - 0191-2216
ER -