In this paper, we consider the topic of model reduction for nonlinear
dynamical systems based on kernel expansions. Our approach allows
for a full offline/online decomposition and efficient online computation
of the reduced model. In particular, we derive an a-posteriori state-space
error estimator for the reduction error. A key ingredient is a local
Lipschitz constant estimation that enables rigorous a-posteriori
error estimation. The computation of the error estimator is realized
by solving an auxiliary differential equation during online simulations.
Estimation iterations can be performed that allow a balancing between
estimation sharpness and computation time. Numerical experiments
demonstrate the estimation improvement over different estimator versions
and the rigor and effectiveness of the error bounds.