arXiv subjects

Sara Dridi

Publications and source records attributed to Sara Dridi.

5 recordsLinked to original sources

arXiv2026

General control of linear cellular automata

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.

nlin.CG↗

arXiv2025

Regional Controllability of Cellular Automata as a SAT Problem

Controllability, one of the fundamental concepts in control theory, consists in guiding a system from an initial state to a desired one within a limited (and possibly minimum) time interval. When the objective is limited to a specific sub-region of the system's domain, the concept is referred to as regional controllability. We examine this notion in the context of Boolean one-dimensional cellular automata of finite length. Depending on the local evolution rule, we investigate whether it is possible to control the evolution of the system by imposing particular values on the boundary conditions. This approach is related to key dynamical properties of CA, specifically chain transitivity and chain mixing. We show that the control problem can be formulated as a Boolean satisfiability (SAT) problem and can thus be addressed using SAT solvers. We also show how finding shortest paths in the configuration graph allows to determine controllability properties. From our observations we can state that only peripherally-linear rules are fully controllable, while for other rules, the reachability ratio, that is, the fraction of controllable pairs of initial and final configurations, is vanishing when the system size grows.

nlin.CG↗

arXiv2025

New Characterization of regional controllability and controllability of deterministic cellular automata via topological and symbolic dynamics notions

This article presents a new characterization of controllability and regional controllability of Deterministic Cellular Automata (CA for short). It focuses on analyzing these problems within the framework of control theory, which have been extensively studied for continuous systems modeled by partial differential equations (PDEs). In the analysis of linear systems, the Kalman rank condition is ubiquitous and has been used to obtain the main results characterizing controllability. The aim of this paper is to highlight new ways to prove the regional controllability and controllability of CA using concepts from symbolic dynamics instead of using the Kalman condition. Necessary and sufficient conditions are given using the notions of chain transitive, chain mixing, trace approximation, transitive SFT and mixing SFT. Finally, we demonstrate that the presence of visibly blocking words implies that the cellular automaton is not controllable.

math.DS↗

arXiv2019

A Graph Theory Approach for Regional Controllability of Boolean Cellular Automata

Controllability is one of the central concepts of modern control theory that allows a good understanding of a system's behaviour. It consists in constraining a system to reach the desired state from an initial state within a given time interval. When the desired objective affects only a sub-region of the domain, the control is said to be regional. The purpose of this paper is to study a particular case of regional control using cellular automata models since they are spatially extended systems where spatial properties can be easily defined thanks to their intrinsic locality. We investigate the case of boundary controls on the target region using an original approach based on graph theory. Necessary and sufficient conditions are given based on the Hamiltonian Circuit and strongly connected component. The controls are obtained using a preimage approach.

nlin.CG↗

arXiv2018

Regional Control of Probabilistic Cellular Automata

Probabilistic Cellular Automata are extended stochastic systems, widely used for modelling phenomena in many disciplines. The possibility of controlling their behaviour is therefore an important topic. We shall present here an approach to the problem of controlling such systems by acting only on the boundary of a target region.

nlin.CG↗