Deadbeat Robust Model Predictive Control: Robustness Without Computing Robust Invariant Sets

Abstract

Deadbeat Robust Model Predictive Control (DRMPC) is introduced as a new approach of Robust Model Predictive Control (RMPC) for linear systems with additive disturbances. Its main idea is to completely extinguish the effect of the disturbances in the predictions within a small number of time steps, called the deadbeat horizon. To this end, explicit deadbeat input sequences are calculated for the vertices of the disturbance set. They generalize to a nonlinear disturbance feedback policy for all disturbances of the set by a barycentric function. Similar to other RMPC approaches, the disturbance feedback policy can be either part of the online optimization (Online DRMPC) or pre-calculated during the design phase of the controller (Offline DRMPC). The main advantage over all other RMPC approaches is that no Robust Positive Invariant (RPI) set has to be calculated, which is often intractable for systems with higher dimensions. Nonetheless, for Online DRMPC and Offline DRMPC recursive feasibility and input-to-state stability can be guaranteed. A small numerical example compares the two versions of DRMPC and demonstrates that the performance of DRMPC is competitive with other state-of-the-art RMPC approaches. Its main advantage is that it is easily extendable to linear time-varying (LTV) and linear parameter-varying (LPV) systems.