You might have a look at this Thesis (Chapter 3 matches your question):

http://theses.gla.ac.uk/2/1/2007luphd.pdf

As I see it, some models involve a singularity so they can not be "inverted", while numeric inverse simulation is still feasible and can evidence the multiplicity of inverse-problem solutions. Inverse simulation is therefore more general than inverse modelling.

Stan Sykora Thanks for the helpful answer.

Dear Yuri,

Reverse simulation is an old technique that has undergone improvements and has become effective, used in dynamic system modeling to find the history of input variables, generate the required output responses from the model and provide reverse solutions. Whereas in the case where the analytical approach to model inversion can indeed present difficulties and inconsistencies.

For more details and information about this subject, i suggest you to see links and attached file on topic.

Inverse modelling and inverse simulation for system ...

https://www.researchgate.net/.../33053483_Inverse_modelling_and...

Feedback methods for inverse simulation of dynamic models for ...

https://www.researchgate.net/.../230582895_Feedback_methods_fo...

Inversion of Vehicle Steering Dynamics with Modelica ... - CiteSeerX

citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.600...

Global Sensitivity Analysis applied to Model Inversion ... - DLR ELIB

https://elib.dlr.de/96495/1/AU_TS_IJPHM_150527_final.pdf

Best regards

Dear Mohamed-Mourad Lafifi , thank you for the reply.

I'm exploring the articles you provided, and that is the direction I wanted to get.

Arash Mousaei Thank you,,