In this paper, we consider the problem of adaptive model predictive control subject to exogenous disturbances. Using a novel set-based adaptive estimation, the problem of robust adaptive MPC is proposed and solved for a class of linearly parameterized uncertain nonlinear systems subject to state and input constraints. Two formulations of the adaptive MPC routine are proposed. A general minmax approach is considered. A Lipschitz-based formulation is also proposed. The closed-loop robust stability of both approaches is demonstrated. The Lipschitz-based approach avoids the need for a minmax optimization problem and is amenable to real-time computation. A simple chemical reactor simulation example is presented that demonstrates the effectiveness of the technique.

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