To verify if the system satisfies the observability property. Several techniques and tools have been developed to study whether a nonlinear system is observable or not. Generally, the observability property study of a nonlinear system are depended values when the expression of determinant (D) are canceled for limited points but not for all operation modes such as in the case of complex expression of determinant.
Dear Zoheir,
We can say that, there some observability implicit properties and other explicit for bilinear system and also for nonlinear system with some conditions. Here are some papers that explain this fact.
-Dynamic Systems Research - ResearchGate
https://www.researchgate.net/topic/Dynamic-Systems
-Observability for Switched Linear Systems - Semantic Scholar
https://pdfs.semanticscholar.org/.../638a4e2392c4afdd61addc4d87...
-CONEWISE LINEAR SYSTEMS - Semantic Scholar
https://pdfs.semanticscholar.org/.../ab0a31155cb5deddc2091c28f0...
-The Dynamic Bearing Observability Matrix Nonlinear ... - HAL-Inria
https://hal.inria.fr/hal-01721774/file/2018_icra_schiano.pdf
-Processes | Free Full-Text | Structural Properties of Dynamic Systems ...
www.mdpi.com/2227-9717/5/2/29/htm
-State estimation of the three-tank system using a multiple model - Hal
https://hal.archives-ouvertes.fr/hal-00977494/document
Best regards
Dear Zoheir,
you are correct. One alternative is to look at a condition number (of the observability matrix) averaged along a trajectory (hence over a large number of operating conditions), instead of just computing the rank of the observability matrix. Christophe Letellier and I have done work on this for the last 20 years. The following papers are good starting points:
Article Relation Between Observability and Differential Embeddings F...
Article Observability of multivariate differential embeddings
An approximate approach based on data can be found here:
Article Investigating observability properties from data in nonlinear dynamics
Regards.
Luis Aguirre
Dear Dr Luis and Dr Lafifi,
Thanks alot for your comments.
I'm very interesting in your works on Observability Dr Luis.
Regards
Cheers Zoheir,
You will find some Matlab (most) or Julia (few) scripts available on Research Gate e.g.
https://www.researchgate.net/project/Scripts-on-Nonlinear-Dynamics (see first items)
that help you see how to compute observability coefficients in some simple cases.
Enjoy!
Luis
Dear Luis,
Many thanks for these useful links. Hoping to work together soon on observabilty study n electrical systems (electric machines ..).
Best regards
Z. Tir
- Badges
- Science topic