overview of related techniques is given in[@Hutchison.2008]. Furthermore, the authors present a support-vector regression to separate the domains with hyperplanes of the form $$\label{eq:pwa-svr}
    h(x) = \sum_{i=1}^{N}(\beta_i k_c (x,x_i) + b_c) = 0 ,$$ with $N$ samples of p-dimensional data $x = [x_1, ..., x_N]$, kernel function $k_c(.,.)$ and tunable parameters $\beta_i, b_c$. The sign of $h$ gives the classification.

### Black-box-techniques.

An alternative approach would be to use neural networks to learn the system dynamics, but the resulting models are usually difficult to check for plausibility and stability, which poses further problems for industrial applications[@Ljung_BlackBox_2001].

Hysteresis Modeling {#hysteresisModeling}
-------------------

Whenever a system’s behavior is not only depending on its current internal states, but also on its past trajectory, the system is called hysteretic. This nonlinear effect occurs in nature phenomena like in magnetization of ferromagnetic materials, but also in artificial systems like two-point controllers. The Hungarian physicist Ferenc Preisach presented the first suitable model to describe hysteretic behavior of magnetism in 1935[@Preisach.1935; @PreisachInMemorial]. His hysteron-operator allows for approximation of natural hysteresis using weighted stairs. The relay operator $R_{\alpha, \beta}$, also called relay hysteron, is expressed by Eq. and illustrated in Fig.\[fig:preisachRelay\]. $$\label{eq:relayHysteron}
    y(x) = \begin{cases}
    1, & \text{if $x 