Model Predictive Control for linear uncertain systems using Pointwise Integral Quadratic Constraints

When controlling safety-critical systems with uncertain components, constraint satisfaction is not only vital but also a major challenge. Model predictive control (MPC) is a common solution to satisfy strict state and input constraints. However, on its own it is not able to deal with uncertainties. Hence, it is necessary to robustify this controller. With this aim, recently contributions have been provided on a tube-based robust MPC scheme for state and input constrained linear systems subject to dynamic uncertainties described by ρ-hard integral quadratic constraints (IQCs). Nonetheless, often ρ-hard IQCs description is too general while uncertainties can be more specifically described by pointwise IQCs. This work is intended to exploit this specific information to improve the existing approach. In particular, the original work shows that the model error between the real uncertain system and the nominal prediction model is bounded by an exponentially stable scalar system. In our work we prove that exploiting the additional information on the uncertainty we can obtain a tighter and simpler bound which results in a set of improvements. In a numerical example, we show these improvements that our result guarantees in terms of computation and in terms of effort needed by the MPC controller.