Optimal and suboptimal 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. In particular we are interested in optimal control, which is rather demanding in computational terms, so we present also a less demanding suboptimal method. Finally, we present an example of optimal control with avoidance.