Kalman Condition and New Algorithm Approach for Regional Controllability of Peripherally-linear Elementary Cellular Automata via Boundary Actions

We formalize the problem of regional controllability of cellular automata (CA) models, when the control is applied to the boundaries of the whole domain. We deal here with one-dimensional, deterministic CA. We show that the control is always possible if the evolution rule depends linearly on at least one of the bordering sites of the neighborhood. The necessary and sufficient conditions are proved by means of the known Kalman criterion. We also report an algorithm to control a subregion of the whole domain by applying the control on the boundaries for a peripherally-linear CA. The obtained results are illustrated by some examples and provided to support the theoretical results. The illustrative examples focused for simplicity, on elementary CA, but can be extended to more general CA.