Wienerization of systems in nonlinear control canonical normal form

We extend the concept of model approximation via wienerization to systems in nonlinear control canonical normal form. We elaborate on the conditions for, and implications of, analytically separating nonlinear input affine dynamical systems in state space form in a static part plus a dynamic one. In doing so, we discuss under which conditions Wiener models may approximate the resulting models well. More precisely, we report that a specific bijective transformation of the original nonlinear model will separate the system into a multidimensional state space structure for which it is possible to compare nonlinear Wiener control against linear control for underactuated nonlinear systems. We finally assess how the former type of control has better closed-loop performance than the latter by means of quantitative examples.