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# Distributed Identification of Nonlinear Systems using Regularization[edit]

**Author**: Radek Beňo

This thesis deals with a new method of identifying nonlinear systems which consist of subsystems called components. The identification problem is here understood as a process of parameters’ calibration of nonlinear systems with fixed structure. The whole work deals with the calibration of parameters of nonlinear systems in steady states. One of the greatest contribution of the work is the component´regularization methodology, which mainly brings better numerical stability of the solution. The presented algorithm is distributed and decomposes the original problem according to the primal decomposition to a series of simpler subproblems, in which one particular steady state of the system is solved, i.e. fitted to the data, according to a given global parameter vector. These subproblems can be solved independently of each other, a global optimizer collects these individual contributions and iteratively changes the parameter’s values according to an optimization criterion. Regularized components support the calibration process in particular by correct definition of the domain of the model’s validity, i.e. the area where the model is numerically well conditioned, and numerical stability is further strengthened by introduction of additional variables that constrain the input, output and internal signals of components. These additional constraints limit the propagation of nonphysical signal values across the entire system model. A Mean-Value Model has been chosen as a type of system model over which distributed optimization works, which makes possible not only to model the basic physical phenomena of the system, but also to use it well within the framework of the further system control design. The presented method is demonstrated in this thesis on a specific example of the calibration of the non-linear model of a Diesel internal combustion engine.

**Radek Beňo**, mailto:benorade@fel.cvut.cz