The problem of robust adaptive predictive control for a class of discrete-time. nonlinear systems is considered. First, a parameter estimation technique, based on an uncertainty set estimation, is formulated. This technique is able to provide robust performance for nonlinear systems subject to exogenous variables. Second, an adaptive MPC is developed to use the uncertainty estimation in a framework of min-max robust control. A Lipschitz-based approach, which provides a conservative approximation for the min-max problem, is used to solve the control problem, retaining the computational complexity of nominal MPC formulations and the robustness of the min-max approach. Finally, the set-based estimation algorithm and the robust predictive controller are successfully applied in two case studies. The first one is the control of anonisothermal CSTR governed by the van de Vusse reaction. Concentration and temperature regulation is considered with the simultaneous estimation of the frequency (or pre-exponential) factors of the Arrhenius equation. In the second example, a biomedical model for chemotherapy control is simulated using control actions provided by the proposed algorithm. The methods for estimation and control were tested using different disturbances scenarios. (C) 2016 Published by Elsevier Ltd.