Identifying discrete event Boolean models from measurement data is a current field of research with many concurring aproaches, depending on many assumptions, e.g. about the measurements, and the structure of the model. In this project, identification of a hybrid model with the help of continuous but normalized data is investigated. The model class is given by discrete time state space models with Zhegalkin Polynomials as RHS. These polynomials have the property that they take Boolean values it the evaluation points are also Boolean, i.e. this class is isomorphic to Boolean functions. On the other hand, the models can be interpreted as well in the continuous domain, thus they are able to generate trajectories in a normalized continuous state space.

The identification problem can be posed straight forward as sum of least square error minimization, which leads to a mixed integer quadratic problem. This is solved by classical means of branch and bound methods with standard tools, here CPLEX. The resulting model is hybrid in the sense that it could generate Boolean as well as continuous trajectories of the system under investigation. The method has been applied firstly to gene expression modelling - in her PhD, Saadia Faisal was concerned with a special problem of Zhegalkin Identification from yeast gene expression data.

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