Controllability analysis of one-and two-dimensional additive real-valued cellular automata

Abstract

In this paper, we study the regional controllability of one-and two-dimensional additive real-valued cellular automata with periodic, fixed, and reflective boundary conditions. The global transition functions of cellular automata are formulated in the matrix form to update the cofiguration. These results are applied to derive and prove the sufficient conditions of regional controllability for these additive cellular automata. In addition, the formulae of the control vectors and control vectors with least-norm for which the additive cellular automata are controllable have been obtained. The illustrations of simulation examples are provided to support the theoretical results.