Flatness-Based Identification of Nonlinear Dynamics

The identification of a nonlinear system model given only measurement data is a frequently encountered task. Uncovering the structure of differential equations as system model alongside with the determination of the optimal parameters is still problem under investigation. Assuming a differentially flat system under investigation, an algorithm for single input single output systems is proposed that faces this identification task. To find a proper state space model, an iterative strategy is presented expanding an initial solution in every step. Harnessing only the measurement data and not their time derivatives a criterion is proposed to select promising extensions to the model avoiding extensive simulation studies on possible model structures. Applying a subset selection reduces the complexity of the resulting models and avoids overfitting. To show the capability of the presented approach to identify a nonlinear state space model from data, a simulation example is presented.