In this paper, we introduce an online safe learning-based Model Predictive Control (MPC) approach. This approach, which we call the ”compatible model approach”, consists of building two models of the system. The first is a piecewise interval-valued over-approximation of the system, and the second is a single-valued piecewise multi-affine estimation of the system’s dynamics. The first model is used to find the set of safe actions at each state, whereas the second is used to choose -out of those safe actions- the input that minimizes a given cost function. For the first model, we use the -assumed known- bounds on the derivative of the dynamics to update the model. The second model should be contained in the first to ensure the feasibility of the MPC scheme everywhere (Hence, the name compatible). Both models can be updated online. We are able to do that because each new transition updates the models locally. We present a test case where we train a mobile robot at low speeds, then navigate it in an environment while avoiding obstacles and collecting new data to learn its dynamics at high speeds.