Information Technology Reference
In-Depth Information
Remark3. For all the considered examples, periodic boundary conditions were
used. It should be noted that for both one and two dimension, the necessary time
T to reach the desired state for extracting CA's rules is less than for finding the
control. The search space in the first case is bigger than in the second one. We
suppose that time horizon T is not fixed. The constraint of fixing T a priori
seems to be very restrictive and makes the problem harder.
time=0
time=4
time=8
w
time=12
time=16
time=18
Fig.4. EvolutionofthecontrolledCA.Thedesiredstateisachievedonthesubregion
ω = {c i,j ,| 4 i,j 6 } attime T =18.
6ConcludingRemarks
Many analysis and control problems via CA's models are still open because of
the complexity of CA's behaviour even described by simple local rules. Some
numerical approaches has been successfully tested to solve simple and particu-
lar problems related to controllability, spreadability and identification of CA's
models [7, 8, 12, 9]. In this paper, the problem of regional controllability of CA's
has been considered and a computational approach based on genetic algorithms
has been proposed and implemented for various examples. Our main goal is to
illustrate the ability of CA's models to perform computational tasks that are
di " cult to do with numerical analysis of partial differential equation (PDE). In
PDE modelling, the problem of regional controllability has been simulated only
for one dimension. The 1D considered example allows to compare CA's and PDE
approaches. The 2D case is very illustrative because no simulation has been done
in two-dimensional systems with PDE models.
With the aim of studying all the aspects of systems theory by means of
CA's models, the present paper constitues an interesting outline. It goes without
saying that much can still be done in this connection.
References
1.Adamatzky,A.:IdentificationofCellularAutomata.Taylor&FrancisEd.(1994)
Search WWH ::




Custom Search