Observability of Nonlinear Dynamical Systems over Finite Fields
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916191019204608 |
|---|---|
| author | Anantharaman, Ramachandran Sule, Virendra |
| author_facet | Anantharaman, Ramachandran Sule, Virendra |
| contents | This paper discusses the observability of nonlinear Dynamical Systems over Finite Fields (DSFF) through the Koopman operator framework. In this work, given a nonlinear DSFF, we construct a linear system of the smallest dimension, called the Linear Output Realization (LOR), which can generate all the output sequences of the original nonlinear system through proper choices of initial conditions (of the associated LOR). We provide necessary and sufficient conditions for the observability of a nonlinear system and establish that the maximum number of outputs sufficient for computing the initial condition is precisely equal to the dimension of the LOR. Further, when the system is not known to be observable, we provide necessary and sufficient conditions for the unique reconstruction of initial conditions for specific output sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Observability of Nonlinear Dynamical Systems over Finite Fields Anantharaman, Ramachandran Sule, Virendra Systems and Control Dynamical Systems This paper discusses the observability of nonlinear Dynamical Systems over Finite Fields (DSFF) through the Koopman operator framework. In this work, given a nonlinear DSFF, we construct a linear system of the smallest dimension, called the Linear Output Realization (LOR), which can generate all the output sequences of the original nonlinear system through proper choices of initial conditions (of the associated LOR). We provide necessary and sufficient conditions for the observability of a nonlinear system and establish that the maximum number of outputs sufficient for computing the initial condition is precisely equal to the dimension of the LOR. Further, when the system is not known to be observable, we provide necessary and sufficient conditions for the unique reconstruction of initial conditions for specific output sequences. |
| title | Observability of Nonlinear Dynamical Systems over Finite Fields |
| topic | Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2404.02336 |