  We propose Kernel Predictive Control (KPC), a learning-based predictive
control strategy that enjoys deterministic guarantees of safety.
Noise-corrupted samples of the unknown system dynamics are used to learn
several models through the formalism of non-parametric kernel regression. By
treating each prediction step individually, we dispense with the need of
propagating sets through highly non-linear maps, a procedure that often
involves multiple conservative approximation steps. Finite-sample error bounds
are then used to enforce state-feasibility by employing an efficient robust
formulation. We then present a relaxation strategy that exploits on-line data
to weaken the optimization problem constraints while preserving safety. Two
numerical examples are provided to illustrate the applicability of the proposed
control method.
