Dynamic uncertainties in model predictive control: Guaranteed stability for constrained linear systems

In this work, we propose a tube-based model predictive control (MPC) scheme for state and input constrained linear systems that are subject to dynamic uncertainties de-scribed by integral quadratic constraints (IQCs). We extend the framework of verifying exponential decay rates with IQCs in order to derive an exponentially stable scalar system that bounds the error between the nominal prediction model and the actual unknown system. In the proposed MPC scheme, this error bounding system is predicted together with the nominal model to define the size of the tube. We prove that this scheme achieves robust constraint satisfaction and input-to-state stability, and we demonstrate the flexibility of dynamic tubes in a numerical example.