A robust adaptive model predictive control framework for nonlinear uncertain systems

Summary In this article, we present a tube‐based framework for robust adaptive model predictive control (RAMPC) for nonlinear systems subject to parametric uncertainty and additive disturbances. Set‐membership estimation is used to provide accurate bounds on the parametric uncertainty, which are employed for the construction of the tube in a robust MPC scheme. The resulting RAMPC framework ensures robust recursive feasibility and robust constraint satisfaction, while allowing for less conservative operation compared with robust MPC schemes without model/parameter adaptation. Furthermore, by using an additional mean‐squared point estimate in the objective function the framework ensures finite‐gain stability w.r.t. additive disturbances. As a first contribution we derive suitable monotonicity and nonincreasing properties on general parameter estimation algorithms and tube/set‐based RAMPC schemes that ensure robust recursive feasibility and robust constraint satisfaction under recursive model updates. Then, as the main contribution of this article, we provide similar conditions for a tube‐based formulation that is parametrized using an incremental Lyapunov function, a scalar contraction rate and a function bounding the uncertainty. With this result, we can provide simple constructive designs for different RAMPC schemes with varying computational complexity and conservatism. As a corollary, we can demonstrate that state of the art formulations for nonlinear RAMPC are a special case of the proposed framework. We provide a numerical example that demonstrates the flexibility of the proposed framework and showcase improvements compared with state of the art approaches.