This work considers linear systems affected by uncertain parameters and additive disturbances. An adaptive model predictive control (MPC) framework is introduced, which can be used with two different parameterizations of state tubes. In this framework, set-membership identification is used to reduce parameter uncertainty online. A novel technique is proposed to formulate a prediction of the set-membership identification within the MPC optimization problem. A predicted worst case cost is used as the MPC objective to enable-performance based dual control. An extension of the algorithm to an uncertain time varying systems is also presented. The performances of the proposed methods and state-of-the-art techniques are compared using a numerical example
