Robust adaptive MPC for constrained uncertain nonlinear systems

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.