  We present a Model Predictive Control (MPC) strategy for unknown input-affine
nonlinear dynamical systems. A non-parametric method is used to estimate the
nonlinear dynamics from observed data. The estimated nonlinear dynamics are
then linearized over time varying regions of the state space to construct an
Affine Time Varying (ATV) model. Error bounds arising from the estimation and
linearization procedure are computed by using sampling techniques. The ATV
model and the uncertainty sets are used to design a robust Model Predictive
Control (MPC) problem which guarantees safety for the unknown system with high
probability. A simple nonlinear example demonstrates the effectiveness of the
approach where commonly used linearization methods fail.
