Observer design for Boolean control networks with unknown inputs

In this paper, multi-input multi-output Boolean control networks are considered as polynomial discrete-time systems in the Galois field 2. Two algorithms are proposed to design observers, able to recognise the state and the input of the system in finite time, without any requirement on the structure of the Boolean control network. It is shown that such procedures can be used, in a wholly probabilistic framework, to estimate the state and the input, even when random noise is superimposed to the available measures. The interest in these methods relies on biological applications, as, for instance, regulatory networks, where the state and the input of the system need to be estimated from scarce and noisy data.