Інтервальний оцінювач стану для лінійних систем з відомою структурою
It is often required to control a system whose state is not observable directly. Instead, there are indirect incomplete and noised measurements of its state. In such situation it is required to estimate current system’s state from these indirect measurements first in order to control the system. For...
Saved in:
| Date: | 2023 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2023
|
| Subjects: | |
| Online Access: | https://jais.net.ua/index.php/files/article/view/109 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Problems of Control and Informatics |
Institution
Problems of Control and Informatics| Summary: | It is often required to control a system whose state is not observable directly. Instead, there are indirect incomplete and noised measurements of its state. In such situation it is required to estimate current system’s state from these indirect measurements first in order to control the system. For this purpose the Kalman filter is the long established and classical approach on estimation of linear systems state from indirect measurements. It is recursive by desin, and thus indirectly takes into account the whole previous history of measurements. Here we explore an alternative approach: estimation with measurements on a limited historic horizon. The article first discusses application of the generalized linear least squares (GLLS) estimator to this problem and conditions under which it is appropriate to use this method. For situations when it is not fully appropriate, we propose a way to represent the GLLS estimator as a quadratic cone programming problem which helps producing its modifications tuned for various nonstandard linear system designs. The article also explores various properties and behavior of the GLLS estimator and its modifications. For instance, it is completely expectable that such estimators demonstrate diferent precision with different number of historic measurements considered. Thus, application of the absolute condition number of the GLLS estimator to choosing an optimal horizon length was explored. It was demonstrated how the absolute condition number of GLLS, while being a hard limit on estimation precision, also limits expected value of error norm. Choice of the best horizon length was discussed from both of these points of view. For situations when best possible estimation precision is still not enough, a regularization method was proposed. Pros and cons of this regularization method and a way to make an informed choice regarding the degree of regularization was explored. The theoretical results were confirmed with computational experiments. |
|---|