General control of linear cellular automata
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915932200239104 |
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| author | Bagnoli, Franco Dridi, Sara Sellami, Bassem Mouakher, Amira Yacoubi, Samira El |
| author_facet | Bagnoli, Franco Dridi, Sara Sellami, Bassem Mouakher, Amira Yacoubi, Samira El |
| contents | In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the ability to determine whether there exists a control input that can steer a dynamical system from an initial state to a desired final state within a finite time horizon. There is a general theory for controlling linear or linearizable system, but it cannot be applied to discrete systems like cellular automata, which is the problem of that we address in this paper. We develop a general theory for linear (and affine) cellular automata, and apply it to examples of one-dimensional and two-dimensional Boolean cases. We introduce the concept of controllability matrix and show that controllability holds if and only if the controllability matrix is invertible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10076 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | General control of linear cellular automata Bagnoli, Franco Dridi, Sara Sellami, Bassem Mouakher, Amira Yacoubi, Samira El Cellular Automata and Lattice Gases Systems and Control In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the ability to determine whether there exists a control input that can steer a dynamical system from an initial state to a desired final state within a finite time horizon. There is a general theory for controlling linear or linearizable system, but it cannot be applied to discrete systems like cellular automata, which is the problem of that we address in this paper. We develop a general theory for linear (and affine) cellular automata, and apply it to examples of one-dimensional and two-dimensional Boolean cases. We introduce the concept of controllability matrix and show that controllability holds if and only if the controllability matrix is invertible. |
| title | General control of linear cellular automata |
| topic | Cellular Automata and Lattice Gases Systems and Control |
| url | https://arxiv.org/abs/2604.10076 |