SUMMARY

System identification is the process of building mathematical models of dynamical systems from measurements of input-output data. When linear system identification fails to cap-ture the system dynamics, nonlinear system identification comes into the picture. As linear system identification techniques are well established, the focus of research is gradually shifting to nonlinear system identification. Within the type of nonlinear system models, block-oriented models have gained wide recognition and attention by the system identifi-cation and automatic control community. In general, these models combine linear dynamic parts with static nonlinear parts in various forms.

While the majority of algorithms in the literature require the entire input/output data records, there are some dynamical systems which can not be sampled at a uniform time interval, e.g. only initial and final values are accessible.

The object of this thesis is to deal with the identification of nonlinear dynamic systems, which can be represented by block-oriented models on the basis of empirical data i.e.incomplete measurements of the state variables. As the problem is highly undetermined,the nonlinear function will be modeled using a piecewise linear function for simplicity, and to reduce the number of unknown variables. Further, the Laplacian regularization will be incorporated in the optimization problem to alleviate the lack of data and smooth the piecewise linear model.

A benefit of using piecewise linear representation for the nonlinear static function is the possibility to approximate a discontinuous static function without embedding an incorrect prior model that might lead to underfitting or poor results. Convergence analysis will be established for the proposed algorithm-and its effectiveness-will be validated through sporadic visual position measurements from a camera mounted on the Georgia Tech miniature autonomous blimp.